Elaine Chao, Trump’s transportation secretary, resigns along with other officials.

President Trump seems to have surrendered his ferocious effort to hang onto power on Thursday after Congress formally accepted the victory of President-elect Joseph R. Biden, but the nation’s government remained in disarray following a mob attack on the Capitol that struck at the heart of American democracy.

Mr. Trump kept out of sight and offline even as Facebook locked his account for the remainder of his presidency and more aides and advisers submitted resignations in protest of his incitement of the rioters who stormed the Capitol to temporarily block the counting of the Electoral College votes.

But in a written statement, he conceded that he would hand over power to Mr. Biden on Jan. 20. “Even though I totally disagree with the outcome of the election, and the facts bear me out, nevertheless there will be an orderly transition on January 20th,” Mr. Trump said in the statement issued shortly after Congress dismissed his allies’ objections to the electors in the pre-dawn hours.

The statement had to be released through an aide’s Twitter account since the president’s own had been suspended for encouraging the crowds that ransacked the Capitol. The president has not appeared in person since then to confirm his commitment to its words, leaving some uncertainty about what could still happen in the 13 days left in his presidency.

The angry aftermath of the invasion of the Capitol had Democrats and even some Republicans talking about whether Mr. Trump should not be allowed to finish his term but rather removed under the disability clause of the 25th Amendment or through a second impeachment.

“This president should not hold office one day longer,” said Senator Chuck Schumer of New York, who will become the majority leader with the seating of two new Democratic senators elected in Georgia this week. “The quickest and most effective way — it can be done today — to remove this president from office would be for the vice president to immediately invoke the 25th Amendment. If the vice president and the Cabinet refuse to stand up, Congress should reconvene to impeach the president.”

The likelihood of either happening seemed remote but some Republicans joined in the call. “All indications are that the president has become unmoored not just from his duty nor even his oath but from reality itself,” said Representative Adam Kinzinger of Illinois, who has been a critic of the president. “It’s time to invoke the 25th Amendment and to end this nightmare.”

Mick Mulvaney, a former White House chief of staff who had been serving as a special envoy for Mr. Trump until he resigned following the mob attack, said the discussion was understandable given the president’s behavior.

“It does not surprise me at all that the 25th Amendment is being discussed,” he told CNBC. Mr. Mulvaney said the president had become increasingly erratic. “Clearly he is not the same as he was eight months ago and certainly the people advising him are not the same as they were eight months ago and that leads to a dangerous sort of combination as you saw yesterday.”

In addition to Mr. Mulvaney, more advisers to the president and administration officials quit in protest, bringing the 11th-hour resignations to more than a half dozen. Former Attorney General William P. Barr, once one of the president’s most important defenders until resigning himself last month, said in a statement to The Associated Press that the president’s actions were a “betrayal of his office and supporters” and that “orchestrating a mob to pressure Congress is inexcusable.”

Even as the wreckage of the attack was being swept away in the Capitol, questions were being asked about how security for the building could be overwhelmed by the mob given that it was well known that Mr. Trump’s supporters planned to rally in Washington on the day of the Electoral College count. Four people died, including a woman who was shot and three others who suffered medical conditions.

Defying the pressure, Congress proceeded to validate Mr. Biden’s victory in a nearly all-night session, voting down Mr. Trump’s allies who objected to electors from two key states. Six Republicans in the Senate and 121 in the House voted to block electors from Arizona while seven senators and 138 House members voted against electors from Pennsylvania.

It was then left to Vice President Mike Pence, who had rebuffed Mr. Trump’s demand that he assert the power to unilaterally block confirmation of the election result as the president of the Senate and presiding officer of the count, to formally announce the results.

“The announcement of the state of the vote by the president of the Senate shall be deemed a sufficient declaration of the persons elected president and vice president of the United States, each for the term beginning on the 20th day of January 2021, and shall be entered together with a list of the votes on the journals of the Senate and the House of Representatives,” Mr. Pence said at 3:41 a.m.

With that dry ritualistic language mandated by parliamentarians, Mr. Pence officially finalized the defeat of his own ticket and Mr. Biden’s coming ascension to the Oval Office.

President-elect Joseph R. Biden Jr. on Thursday plans to introduce his pick for attorney general, Judge Merrick B. Garland, and three other nominees for top positions at the Justice Department, which experienced a period of increased politicization under President Trump.

Mr. Biden will introduce the nominees at an event in Wilmington, Del., in the afternoon. The president-elect officially announced Judge Garland’s selection in a news release early Thursday morning, after news of his selection became public a day earlier.

The attorney general had been the most prominent position that was still unfilled with Inauguration Day approaching.

Judge Garland currently serves on the U.S. Court of Appeals for the District of Columbia Circuit. President Barack Obama nominated him to the Supreme Court in 2016 after the death of Justice Antonin Scalia, but Senate Republicans blocked his nomination.

Mr. Biden also named three other top Justice Department officials in addition to Judge Garland. The president-elect will nominate Lisa Monaco, a former homeland security adviser to Mr. Obama, as deputy attorney general; Vanita Gupta, who led the Justice Department’s civil rights division under Mr. Obama, as the No. 3 official; and Kristen Clarke, a civil rights lawyer, as assistant attorney general for civil rights.

“Our first-rate nominees to lead the Justice Department are eminently qualified, embody character and judgment that is beyond reproach, and have devoted their careers to serving the American people with honor and integrity,” Mr. Biden said in a statement. “They will restore the independence of the department so it serves the interests of the people, not a presidency; rebuild public trust in the rule of law; and work tirelessly to ensure a more fair and equitable justice system.”

Elaine Chao, the secretary of transportation, is resigning after President Trump’s incitement of a mob that stormed the U.S. Capitol on Wednesday, she announced in a letter posted on Twitter.

Ms. Chao — who is married to Senator Mitch McConnell, the Republican leader — is the first cabinet official to join a growing exodus of administration officials in the final days of the Trump administration: largely symbolic resignations given that most would have been out of jobs with the change of administration anyway.

In the letter, she said that she would leave her post on Jan. 11 and that her office would cooperate with President-elect Joseph R. Biden Jr.’s nominee for transportation secretary, Pete Buttigieg.

“Yesterday, our country experienced a traumatic and entirely avoidable event as supporters of the president stormed the Capitol building following a rally he addressed,” Ms. Chao wrote. “As I’m sure is the case with many of you, it has deeply troubled me in a way that I simply cannot set aside.”

The acting chairman of the White House Council of Economic Advisers, Tyler Goodspeed, also resigned his position on Thursday. Mick Mulvaney, Mr. Trump’s former acting chief of staff, resigned his post as special envoy to Northern Ireland on Wednesday night, and the president’s deputy national security adviser, Matt Pottinger, stepped down as well, a person familiar with his decision said Thursday.

“The events of yesterday made my position no longer tenable,” Mr. Goodspeed said in a brief morning interview, after informing the White House chief of staff, Mark Meadows, of his decision.

In an interview with CNBC on Thursday morning, Mr. Mulvaney, who was pushed out as acting chief of staff in March, said he had called Secretary of State Mike Pompeo the night before to tell him.

“I can’t stay here, not after yesterday,” Mr. Mulvaney said, tying his resignation to the violence at the Capitol. “You can’t look at that yesterday and think ‘I want to be part of that’ in any way, shape or form.”

Mr. Pottinger was one of the key advocates inside the White House for a more robust response to the coronavirus early last year and was ridiculed by co-workers for wearing a mask to work, according to a piece in The New Yorker late last month.

Other officials are considering resigning in response to Wednesday’s siege at the Capitol as well. But one of those who had been said to be considering leaving, the national security adviser, Robert C. O’Brien, plans to stay, in part out of concern about leaving no one in the government at its tumultuous end, another person familiar with events said.

Mr. Mulvaney on Thursday praised administration officials who defended Vice President Mike Pence, who certified the Electoral College vote despite Mr. Trump pressuring him to overturn the results of the election.

Mr. Mulvaney said he anticipated there would be more resignations and praised the small group of people who had quit on Wednesday.

“Those who choose to stay, and I have talked with some of them, are choosing to stay because they’re worried the president might put someone worse in,” said Mr. Mulvaney, who once publicly acknowledged and defended the president’s move to suspend $391 million in aid to Ukraine in exchange for investigations into his political rivals, a scheme at the heart of Mr. Trump’s impeachment.

In the hours after Mr. Trump took to social media on Wednesday to openly condone the violence at the Capitol, he found himself increasingly isolated as White House officials began submitting their resignations, with more expected to follow suit.

Stephanie Grisham, the former White House press secretary who served as the chief of staff to Melania Trump, the first lady, submitted her resignation after the violent protests. Ms. Grisham has worked for the Trumps since the 2016 campaign and is one of their longest-serving aides.

Rickie Niceta, the White House social secretary, also said she was resigning, according to an administration official familiar with her plans who was not authorized to speak publicly. And Sarah Matthews, a deputy White House press secretary, also submitted her resignation, saying in a statement that she was “deeply disturbed by what I saw today.”

And John Costello, one of the country’s most senior cybersecurity officials, also resigned Wednesday, telling associates that the violence on Capitol Hill was his “breaking point” and, he hoped, “a wake up call.”

Mr. Goodspeed has led the council since July and has served in the Trump administration in several economic positions since 2017. His departure leaves no remaining members of the council, which traditionally consists of a chair and two other members. Its last Senate-confirmed chairman, Kevin Hassett, left the White House in 2019. Former Acting Chairman Tomas Philipson departed in June.

Mr. Goodspeed said he was committed to helping the staff at the council assist in the transition to the incoming members of President-elect Joseph R. Biden Jr.’s council. He also said he remained proud of the administration’s pre-pandemic economic record, and of its policy response to the pandemic recession.

Outside of goverment, a Pennsylvania lawyer who worked for the Trump campaign withdrew on Thursday, saying in a court filing that his services had been used “to perpetrate a crime.”

The lawyer, Jerome Marcus, has been an attorney on a case in federal court involving the access of Republican poll watchers in Philadelphia.

In a statement, Mr. Marcus said the case he filed and others like it “were used by President Trump to incite people to violence. I refer specifically to his urging people to come to Washington for a ‘wild’ protest. I want absolutely no part of that.”

Nicole Perlroth contributed reporting.

Senator Chuck Schumer of New York, the Democratic leader, called on Thursday for President Trump’s immediate removal from office for his role in urging on the violent mob that overtook the Capitol a day before, disrupting the ratification of President-elect Joseph R. Biden Jr.’s electoral victory.

“What happened at the U.S. Capitol yesterday was an insurrection against the United States, incited by the president,” Mr. Schumer said. “This president should not hold office one day longer.”

He called on Vice President Mike Pence to invoke the 25th Amendment, which allows him and the Cabinet to wrest the power of the presidency from Mr. Trump. If Mr. Pence would not, Mr. Schumer added, Congress should reassemble to impeach Mr. Trump a second time, even with just days left in his term.

Mr. Schumer was by far the most prominent voice in a growing chorus of Democrats, and a few Republicans, who surveyed the aftermath of Wednesday’s historic events and concluded Mr. Trump was too dangerous to remain in office until Jan. 20, when Mr. Biden is set to be sworn in.

Speaker Nancy Pelosi, who would spearhead any impeachment in the House, had not yet commented on the matter. She was scheduled to hold a news conference at 1 p.m.

Representative Adam Kinzinger, Republican of Illinois, had issued a similar call earlier on Thursday, posting on Twitter that the president had become “unmoored not just from his duty or from his oath but from reality itself.”

His statement followed similar ones by Representatives Charlie Crist and Ted Lieu on Wednesday and a letter signed by 17 Democratic members of the House Judiciary Committee was sent to Mr. Pence calling to invoke the 25th Amendment.

On Thursday morning, a Washington-based law firm, Crowell & Moring, which represents a number of Fortune 500 companies, added their voice to the growing chorus of civic and business leaders calling for the president’s removal. In asking other lawyers to join with them, the firm said that “when it comes to defending our Constitution and our system of laws, we have a special duty and an exceptional perspective.”

Senator Chuck Schumer of New York, the minority leader, said on Thursday that he would fire Michael C. Stenger, the Senate sergeant-at-arms, as soon as Democrats took the majority. The statement was first reported by Politico.

“If Senate Sergeant Arms Stenger hasn’t vacated the position by then, I will fire him as soon as Democrats have a majority in the Senate,” Mr. Schumer said.

As the upper chamber’s sergeant-at-arms, Mr. Stenger is responsible for overseeing the rules of the Senate and maintaining security in both the Capitol and Senate office buildings.

Mr. Stenger, who has held the position since April 2018, spent 35 years in the Secret Service and is a former captain in the Marine Corps.

Mr. Schumer’s statement comes as lawmakers in both chambers and from both parties vowed on Thursday to find out how those responsible for Capitol security allowed a violent mob to infiltrate the Capitol. House Democrats announced a “robust” investigation into the law enforcement breakdown.

Senator Mitch McConnell of Kentucky, the Republican leader, said in a statement that “a painstaking investigation and thorough review,” was needed after the events of Wednesday, which he described as “a massive failure of institutions, protocols, and planning that are supposed to protect the first branch of our federal government.”

Mr. McConnell added that “the ultimate blame for yesterday lies with the unhinged criminals who broke down doors, trampled our nation’s flag, fought with law enforcement, and tried to disrupt our democracy, and with those who incited them.

“But this fact does not and will not preclude our addressing the shocking failures in the Capitol’s security posture and protocols.”

This is a developing story. Check back for updates.

WASHINGTON — The stunning Democratic wins in two Georgia Senate races this week upended Washington’s power structure overnight, providing an unexpected opening to the incoming Biden administration by handing unified control of Congress to Democrats who will be tested by governing with spare majorities.

The victories by the Rev. Raphael Warnock and Jon Ossoff mean that Senator Chuck Schumer, Democrat of New York, will control the Senate floor rather than Senator Mitch McConnell, Republican of Kentucky — the man Democrats have long seen as the main impediment to their legislative ambitions.

They emerged even as a violent siege of the Capitol on Wednesday, egged on by President Trump, reflected the staunch refusal of his supporters to acknowledge President-elect Joseph R. Biden Jr. as the winner of the election, a last gasp of Republican protest before Democrats assume control of the levers of power.

In a wholesale change that will shift the policy agenda overnight, liberal Democrats — including Senator Bernie Sanders of Vermont, the democratic socialist who will now lead the Budget Committee — will lead most Senate panels, rather than conservative Republicans. Legislation from the Democratic-controlled House that had languished in the Senate will now get consideration across the Rotunda.

The abrupt shift in circumstances invigorated Democrats who had been deflated in November when they failed to gain a majority on Nov. 3 despite Mr. Biden’s victory. Given the traditional advantage Republicans have had in Georgia runoff elections, many Democrats had become resigned to the prospect that they would be stymied in their ability to deliver on Mr. Biden’s priorities.

“We sure did not take the most direct path to get here, but here we are,” said Mr. Schumer, happy with the outcome any way he could get it, which put him in reach of fulfilling his ambition of becoming majority leader after six years as the chief of the minority.

While the change in Senate control is momentous, particularly in easing the way for Mr. Biden to fill administration jobs and judicial vacancies, it does not mean that Democrats can have their way on everything — or even most things. The Democratic majority in the House shrank in the last election, emboldening Republicans and giving Speaker Nancy Pelosi less wiggle room in what is most likely her last term.

With the Senate divided 50-50 and Democrats in charge only by the virtue of the tiebreaking power of the vice president, the filibuster also looms large. Democrats will need to attract at least 10 Republicans to advance most bills while contending with demands from the left for bolder action now that their party controls all of Congress.

Democrats conceded the difficulties but still welcomed the reversal of fortune.

“It is not all going to be easy, but it is certainly better than being 52-48 and President Biden playing ‘Mother, May I?’ with Leader McConnell in moving any legislation to the floor,” said Senator Christopher Coons, Democrat of Delaware, one of the incoming president’s closet allies on Capitol Hill.

Still, Mr. McConnell, newly elected to his seventh term, has been in the position of leading the minority before and has proved effective in obstructing Democratic priorities.

SAN FRANCISCO — Facebook on Thursday said it will block President Trump on its platforms at least until the end of his term on Jan. 20, as the mainstream online world moved forcefully to limit the president after years of inaction.

Mark Zuckerberg, Facebook’s chief executive, said in a post that the social network decided to cut off Mr. Trump because a rampage by pro-Trump supporters in the nation’s capital a day earlier, which was urged on by the president, showed that Mr. Trump “intends to use his remaining time in office to undermine the peaceful and lawful transition of power to his elected successor, Joe Biden.”

“We believe the risks of allowing the president to continue to use our service during this period are simply too great,” Mr. Zuckerberg wrote. As a result, he said, Facebook and its photo-sharing site Instagram would extend blocks, first put in place on Wednesday, on Mr. Trump’s ability to post “until the peaceful transition of power is complete.”

The move was part of a widening revolt by social media companies against Mr. Trump, who has used the sites throughout his presidency to rile up his supporters and bully his enemies.

Twitter on Wednesday said it would lock Mr. Trump’s account for 12 hours because he had posted several tweets that violated its rules against calling for violence and discrediting the vote. Snap, the maker of Snapchat, also cut off access to Mr. Trump’s Snapchat account. And YouTube on Thursday implemented a stricter election fraud misinformation policy to make it easier to suspend the president for posting false election claims.

The actions were a striking change for a social media industry that has long declined to take down Mr. Trump’s posts, which were often filled with falsehoods and threats. Facebook and Twitter positioned themselves as defenders of free speech and public discussion, saying it was in people’s interests to see what world leaders posted, even as critics assailed them for allowing misinformation and toxic content to flow unimpeded.

Lawmakers and even employees of the companies said the platforms had waited too long to take serious action against Mr. Trump. At Facebook, dozens of employees noted that the company had only suspended Mr. Trump after Democrats had secured the presidency and control of the Senate, according to people familiar with the internal conversations.

“While I’m pleased to see social media platforms like Facebook, Twitter and YouTube take long-belated steps to address the president’s sustained misuse of their platforms to sow discord and violence, these isolated actions are both too late and not nearly enough,” said Senator Mark Warner, Democrat of Virginia.

The spotlight now falls on Twitter and what it will do with Mr. Trump’s account. The social media service has been Mr. Trump’s preferred megaphone, where he has more than 88 million followers, compared with 35 million on Facebook. Twitter’s locking of Mr. Trump’s account on Wednesday was set to be lifted on Thursday if he complied with the service’s demand to delete several tweets.

Twitter said in a statement that it was continuing to evaluate the situation and whether “further escalation in our enforcement approach is necessary.” On Wednesday, the company had said the risks of keeping Mr. Trump’s commentary live on its site had become too high.

Derrick Johnson, the president and chief executive of the NAACP, praised Facebook’s decision to lock Mr. Trump’s account, and said he urged Twitter to do the same.

“The president’s social media accounts are a petri dish of disinformation, designed to divide and fuel violence at all costs,” Mr. Johnson said.

A spokesman for the White House did not immediately respond to a request for comment.

In recent months, Twitter and Facebook had begun to push back on the president’s posts, adding fact-checking labels to some of his most incendiary statements. Mr. Trump fired back, signing an executive order intended to strip legal protections from the social media companies and claiming they were censoring conservative voices.

At Facebook, Mr. Zuckerberg and other executives had given Mr. Trump significant leeway on his Facebook account, often allowing the president’s false statements to stay up on the network despite heavy criticism.

Mr. Zuckerberg repeatedly said he did not want Facebook to be “the arbiter of truth” in political discourse and that he believed strongly in protecting speech across Facebook, the platform he founded that is now used by more than three billion people globally.

“We did this because we believe that the public has a right to the broadest possible access to political speech, even controversial speech,” Mr. Zuckerberg said in his post on Thursday.

“The current context is now fundamentally different, involving use of our platform to incite violent insurrection against a democratically elected government,” Mr. Zuckerberg said.

Daisuke Wakabayashi and Sheera Frenkel contributed reporting.

The events of the last 48 hours — Tuesday’s Democratic takeover of the Senate and Wednesday’s mob violence at the Capitol by President Trump supporters — fundamentally altered the trajectory of President-elect Joseph R. Biden Jr.’s presidency two weeks before his hand touches the bible.

Once chatty, malaprop-prone and accessible, Mr. Biden has transformed himself into a figure of distance and dignity, taking advantage of the spotlight-hogging futility of Mr. Trump’s attempts to overturn the election. He has been able to quietly assemble a team and plan for the battles ahead.

The violence, in the view of several people in Mr. Biden’s immediate orbit, has mellowed the intensity of Republican opposition to him, especially among the members of the chamber most eager to distance themselves from Mr. Trump’s antics.

Most notable among them: the Senate Republican leader, Mitch McConnell, who had defined unseating President Obama as his primary goal at this point in 2009; and Lindsey Graham, the Republican from South Carolina who has buddied up to both Mr. Biden and Mr. Trump over the years.

There is nothing quite like huddling behind barricaded doors with an armed mob roaming the hallways to rekindle the dying embers of bipartisanship. But nobody expects it to last.

Mr. Trump incited the riot and Mr. Biden, a senator for nearly four decades, is universally regarded as a guardian of the institution — which matters a great deal to people like Mr. McConnell.

What does this mean in the short term? For starters, it is likely to diminish (but not eliminate) opposition to Mr. Biden’s cabinet picks, although big fights loom.

Mr. Graham on Wednesday, for instance, praised Merrick Garland, the president-elect’s choice for attorney general, and other senators have signaled a less combative approach that has not been seen since the days before social media provocation dominated the discourse.

The landscape was dramatically altered even before the riot, with the double triumph of the two Democrats, Raphael Warnock and Jon Ossoff, in the Georgia Senate runoff elections on Tuesday.

The Biden team had quietly downplayed the idea that they would actually win — in part out of superstition, several jittery Democratic aides suggested in the days leading up to the election.

In the most basic sense, the addition of two Democrats means Mr. Biden needs fewer Republican votes and, just as important, has control over which bills are sent to the floor, a major lever of power unappreciated outside of Washington.

But the pressure from Mr. Biden’s left flank to use these powers will be great. Democrats fear a Republican takeover of the House in 2022, and a similar possibility looms in the deadlocked upper chamber.

Many in Mr. Biden’s circle believe he has two years to jam through Democratic priorities, starting with his pledge to pass a $2,000 payment to Americans to ease the economic hardship of the pandemic. That tension — whether to go it alone or wait for compromise — is likely to define his presidency.

“Biden will say all the public things about how he needs to get Republican support, but the truth is that this fundamentally changes the dynamic,” said David Krone, former chief of staff to former Senator Harry Reid, the last Democratic majority leader. “Democrats now control the floor. So he can bring up all kinds of bills that would have been blocked by the Republicans, and force votes on big bills — like a major infrastructure package.”

Then there’s Vice President-elect Kamala Harris, who will have more power as the tiebreaking presiding office in a 50-50 deadlocked Senate.

It will also ensure her visibility as Mr. Biden’s partner and natural successor.

Congress rejected an attempt from Republicans to overturn the will of Pennsylvania voters early Thursday, effectively ending a final attempt from insurgents to turn a loss for President Trump in the state into a win.

The House rejected the challenge by a vote of 282 to 138, after a long debate dragged past 3 a.m. in Washington. A scuffle almost broke out on the chamber floor after Representative Conor Lamb, Democrat of Pennsylvania, delivered a particularly fiery speech in condemnation of the Republican objections.

“That attack today, it didn’t materialize out of nowhere,” Mr. Lamb said. “It was inspired by lies, the same lies you’re hearing in this room tonight, and the members who are repeating those lies should be ashamed of themselves.”

By a vote of 92 to 7, the Senate turned back the Pennsylvania challenge shortly before 1 a.m., as the number of objections to the counting of Electoral College votes dwindled after the mob’s brazen effort to keep President Trump in office, despite his decisive election loss in November.

Those senators voting against the results of the presidential election in Pennsylvania were: Josh Hawley of Missouri, Ted Cruz of Texas, Tommy Tuberville of Alabama, Cindy Hyde-Smith of Mississippi, Roger Marshall of Kansas, Cynthia Lummis of Wyoming and Rick Scott of Florida.

As most Republicans and all Democrats rejected the attempt, Senator Mike Lee, Republican of Utah, forcefully turned back the plot, registering his vote as “hell no.”

Earlier in the evening, lawmakers rejected an attempt to overturn the Arizona electoral slate. The House blocked the attempt with a 303-to-121 vote while the Senate offered a sharper rebuke with a 93-to-6 vote.

After debating the merits of subverting the majority of Arizona voters, lawmakers sped through the certification for several states after at least four Republican lawmakers, including Senator Kelly Loeffler of Georgia, said they had changed their minds and would vote to uphold the Electoral College results after having previously said that they would object to them.

Those voting against the results of the election in Arizona were: Mr. Hawley, Mr. Cruz, Mr. Tuberville, Ms. Hyde-Smith, Mr. Marshall and John Kennedy of Louisiana.

The move by Ms. Loeffler, who lost a special election in Georgia and failed to retain her Senate seat, amounted to one of her last acts in the upper chamber, and she announced her reversal during remarks on the Senate floor after the debate resumed late Wednesday.

Ms. Loeffler’s remarks came after Representative Cathy McMorris Rodgers of Washington and Senator Steve Daines of Montana condemned the actions of Trump loyalists who broke into the Capitol earlier on Wednesday and said they would no longer back an effort by some of their Republican colleagues to throw out the election results.

Ms. McMorris Rodgers’s remarks were particularly pointed.

“Thugs assaulted Capitol Police officers, breached and defaced our Capitol building, put people’s lives in danger and disregarded the values we hold dear as Americans,” Ms. McMorris Rodgers said in a statement, which she released a day after declaring she would object to the vote counts. “To anyone involved, shame on you.”

“What we have seen today is unlawful and unacceptable,” she added. “I have decided I will vote to uphold the Electoral College results, and I encourage Donald Trump to condemn and put an end to this madness.”

Shortly after Ms. McMorris Rodgers announced her decision, Mr. Daines followed suit, saying he, too, would certify electoral votes after having previously signed onto a letter saying he and other Republican senators “intend to vote on Jan. 6 to reject the electors” from some states.

“Today is a sad day for our country. The destruction and violence we saw at our Capitol today is an assault on our democracy, our Constitution and the rule of law, and must not be tolerated,” he said in his new statement Wednesday night.

The first criminal charges against some of the pro-Trump rioters who stormed the Capitol on Wednesday will be filed as early as Thursday, the acting attorney general, Jeffrey A. Rosen, said in a statement.

He added that criminal prosecutors had worked through the evening with police and federal law enforcement officials to identify perpetrators, and that more would be arrested and charged in coming days and weeks.

“Yesterday, our nation watched in disbelief as a mob breached the Capitol building and required federal and local law enforcement to help restore order,” Mr. Rosen said. “The Department of Justice is committed to ensuring that those responsible for this attack on our government and the rule of law face the full consequences of their actions under the law.”

The F.B.I. director, Christopher Wray, also vowed to track down the perpetrators of property destruction at the Capitol, as well as “violent agitators and extremists who use the guise of First Amendment-protected activity to incite violence and wreak havoc,” he said in a statement.

“Let me assure the American people the F.B.I. has deployed our full investigative resources and is working closely with our federal, state, and local partners to aggressively pursue those involved in criminal activity during the events of January 6,” Mr. Wray said. “Our agents and analysts have been hard at work through the night gathering evidence, sharing intelligence, and working with federal prosecutors to bring charges.”

He asked members of the public to provide tips and upload videos of illegal activity at the webpage “FBI Seeking Information Related to Violent Activity at the U.S. Capitol Building.”

At least 52 people have been arrested, including five on weapons charges and at least 26 on the grounds of the U.S. Capitol, according to Robert Contee, chief of the city’s Metropolitan Police Department.

The criticism of the Capitol Police was swift and, in some quarters, unforgiving. It took more than two hours, and reinforcements from other law enforcement agencies, before order was restored to the Capitol on Wednesday.

The officers were easily overwhelmed by the crowds; some law enforcement experts were astonished by the sight of an officer cowering in the crush of pro-Trump extremists and rioters using police shields and metal barricades as battering rams.

“How they were not ready for this today, I have no idea,” said Charles Ramsey, a former D.C. police chief, adding that “they did not have the resources. You have to be able to protect the Capitol. That is not OK.”

Protesters on the left saw a stark double standard, saying they had been hit with rubber bullets, manhandled, surrounded and arrested while behaving peacefully during demonstrations against racial injustice over the summer.

Members of Congress demanded explanations as well. Representative Maxine Waters, a California Democrat, wrote on Twitter. “I warned our Caucus and had an hourlong conversation with the Chief of Police 4 days ago. He assured me the terrorists would not be allowed on the plaza & Capitol secured.”

The chief of the U.S. Capitol Police confirmed on Thursday that an officer had shot and killed a woman inside the Capitol after the building was breached by President Trump’s supporters. He identified the woman as Ashli Babbitt, a former member of the Air Force.

Ms. Babbitt, 35, had been assigned to security units that police Air Force bases, according to military publications. A 2014 article said she had deployed seven times in eight years and achieved the rank of senior airman.

Chief Steven A. Sund of the Capitol Police said the attack on the Capitol “was unlike any I have experienced in my 30 years in law enforcement,” and he defended the actions of the officers as “heroic,” despite widespread criticism over how easily they were overrun by the mob of Trump supporters.

Chief Sund said an officer had shot Ms. Babbitt as the people who had overrun the Capitol “were forcing their way” to a part of the building where members of Congress were sheltering. A spokesman for the Metropolitan Police Department, the local police in Washington, had said on Wednesday that the officer who shot Ms. Babbitt was a plainclothes Capitol Police officer.

In a pair of videos that appeared to capture the shooting, a woman who has a Make America Great Again flag draped around her can be seen stepping up to a ledge next to a door to the Speaker’s Lobby, a long hallway with portraits of former speakers of the House. As soon as she steps up to the ledge next to the door, a loud bang can be heard, and she falls to the ground. As people call for help, she begins to bleed around her mouth and neck.

Chief Sund said his agency had placed the officer who shot Ms. Babbitt on administrative leave and that the officer’s police powers had been suspended. He did not identify the officer.

The Pentagon is deploying more than 5,000 additional National Guard troops from six states to Washington, and the troops will stay through the inauguration later this month, a senior Pentagon official said Thursday.

After pleas from Mayor Muriel Bowser of Washington, the Pentagon mobilized all 1,100 available District of Columbia National Guard troops on Wednesday afternoon to confront the violent mob that had stormed the Capitol. About 340 D.C. National Guard had been called up earlier in the week to help with crowd and traffic control.

An additional 5,100 Guard troops from Virginia, Maryland, New York, Delaware, Pennsylvania and New Jersey are expected to arrive in Washington over the next several days and remain through Jan. 20 for President-elect Joseph R. Biden Jr.’s inauguration, the senior official said.

That will bring the total number of Guard troops in the capital to 6,200.

Pentagon officials said that the additional Guard personnel would support local police and federal law enforcement officers.

In June, some 5,000 Guard troops — from the District of Columbia and a dozen states — were rushed to the streets of the capital to help in the crackdown on mostly peaceful protesters and occasional looters after the killing of George Floyd in police custody.

The actions of law enforcement officials before, during and after a violent breach of the Capitol on Wednesday by a pro-Trump mob were coming into question as images emerged of officers gently escorting rioters to their freedom — and a video showing officers pushing aside barricades used to keep the mob from entering the complex.

The law enforcement agencies responsible for protecting the complex, a patchwork of federal and local agencies led by the 2,000-member Capitol Police force, are already facing scrutiny over their inability to counter the violence despite weeks of none-too-secret planning by the attackers on social media sites like Gab and Parler.

The Capitol Police, which is shielded from the transparency requirements of other federal agencies by law, did not respond to requests for comment on Wednesday. On Thursday morning, Steven Sund, the chief of police, issued a statement vowing “a thorough review of this incident, security planning and policies and procedures.”

“The violent attack on the U.S. Capitol was unlike any I have ever experienced in my 30 years in law enforcement here in Washington, D.C.,” Mr. Sund said. “The USCP had a robust plan established to address anticipated First Amendment activities. But make no mistake — these mass riots were not First Amendment activities; they were criminal riotous behavior.”

Mr. Sund said more than 50 Capitol Police and Washington Metro Police officers had been injured, and several Capitol Police officers were hospitalized with serious injuries. A Capitol Police officer who shot and killed a woman outside the House chamber has been placed on administrative leave while the department investigates.

Representative Maxine Waters, a California Democrat, said on Twitter late Wednesday: “We must investigate the security breach at the Capitol today. I warned our Caucus and had an hour long conversation with the Chief of Police 4days ago. He assured me the terrorists would not be allowed on the plaza & Capitol secured.” (An earlier version of this briefing item misstated the timing of the events at the Capitol and the statement by the Capitol Police. The Capitol was stormed on Wednesday, not Tuesday, and the Capitol Police issued their response on Thursday, not Wednesday.)

When debate over certification of the presidential election resumed amid shattered glass, lawmakers from both parties praised the heroism of the officers who battled with violent protesters.

But many in the mob, which numbered in the hundreds, appeared to act with the abandon of lawbreakers confident they would not be held accountable.

Some gleefully snatched and smashed cameras from journalists, others smiled without masks for selfies, and one Richard Barnett, 60, from Gravette, Ark., amiably recounted his invasion of Speaker Nancy Pelosi’s personal office to a reporter after posing for a picture with his feet on her desk.

“Why on earth is this man not under arrest and in prison?” Ben Rhodes, a former speechwriter for President Obama, asked on Twitter.

The contrast between the treatment of the mostly white pro-Trump mob and the massive show of force to counter more peaceful and racially diverse protests against police violence last summer was striking to many.

“It was strange, because it was almost like there was this call to not use force,” Representative Cori Bush, a Democrat from St. Louis, said in an interview with MSNBC shortly after the attack.

Ms. Bush said that the rioters “would have been shot” if they were Black, adding the treatment reflected “white privilege.”

Law enforcement officials told lawmakers on Wednesday that their main priority was to clear the complex quickly, rather than make arrests, so that legislative activity could resume as soon as possible.

As of 9:30 p.m. Wednesday, the last accounting offered by law enforcement agencies, at least 52 people were arrested, including five on weapons charges and at least 26 on the grounds of the Capitol. Most of the arrests were for violating the 6 p.m. curfew, he said, adding that the police would circulate pictures of those sought for breaching the Capitol building.

In addition, pipe bombs were found at the headquarters of both the Republican and the Democratic National Committees and a cooler containing a long gun and Molotov cocktails was discovered on the Capitol grounds, Washington D.C. police officials said.

On Wednesday morning, the F.B.I. posted a web page for tips about individuals involved in the violence, and details of new attacks that might be in the works — allowing citizens to upload digital images of people involved.

Four people lost their lives during the melee in Washington on Wednesday. One of them was Kevin D. Greeson, 55, of Athens, Ala., who collapsed as he stood among a sea of Trump supporters on the west side of the U.S. Capitol.

Mr. Greeson had been talking to his wife on his phone when he fell to the sidewalk. A New York Times reporter watched as emergency personnel rushed to help, furiously performing chest compressions, but were unable to revive him.

In an interview on Thursday, his wife, Kristi Greeson, said authorities contacted her afterward to say that her husband had died of a heart attack. Ms. Greeson said her husband, who was a father of five, had left home on Tuesday, spending the night in Virginia with a friend. She said her husband, who had high blood pressure, was excited to attend the rally, believing the election had been stolen.

“He felt like it was a monumental event in his mind,” she said. “I didn’t want him to go. I didn’t feel like it was safe.”

Ms. Greeson said her husband was a “political junkie” who liked President Trump because he cared about blue collar workers such as Mr. Greeson. But her husband also “saw the good and bad in Trump,” she said.

The others who died included a woman and a man who suffered “medical emergencies” and a woman, identified as Ashli Babbitt, who was shot and killed by the Capitol Police, according to law enforcement officials.

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The Trump supporters pressed through police barricades, broke windows and battered their way with metal poles through entrances to the Capitol. Then, stunningly, they breached the “People’s House” itself, forcing masked police officers to draw their guns to keep the insurgents off the chamber floor.

“I thought we’d have to fight our way out,” said Representative Jason Crow, Democrat of Colorado and a former Army Ranger in Iraq, who found himself captive in the House chamber.

What unfolded at that point, at times on national television, was a tableau of violence and mayhem that shocked the nation, one of the most severe intrusions of the Capitol since the British invaded during the War of 1812 and burned it down.

An armed standoff ensued in the House chamber, with police officers drawing their weapons. A pro-Trump extremist casually monkeyed around at the dais of the Senate. Intruders in Speaker Nancy Pelosi’s suite overturned desks and smashed photos. Others ripped artwork in Senate hideaway offices.

“This is what the president has caused today, this insurrection,” Senator Mitt Romney, Republican of Utah, said as he and other senators were hustled off to a secure location.

Some protesters gawked at the grand and storied building they had flooded while others looked at it with contempt.

“I don’t trust any of these people,” said Eric Martin, 49, a woodworker from Charleston, S.C., as he marveled at the opulence of the Capitol and helped a friend wash pepper spray from his eyes. “Absolute power corrupts absolutely.”

But if some only stared at the Capitol, others resorted to violence. A woman inside the building was shot and later died, the District of Columbia police said, and multiple officers were injured. Two explosive devices were found around noon near the headquarters of the Republican National Committee, then destroyed by a bomb squad. And the federal authorities arrested a 70-year-old man from Alabama near the Capitol in possession of a firearm and materials to make several Molotov cocktails.

By Wednesday evening, the scene outside the Capitol had calmed, after Capitol Police, supplemented by F.B.I. agents and Department of Homeland Security officers with members of the National Guard on their way, squeezed pro-Trump extremists from every corner of the building to the majestic Rotunda, then persuaded them to leave.

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‘We Believe in the Strength of American Democracy,’ Macron Says

Global leaders, including President Emmanuel Macron of France, reacted to the riot in Washington, expressing support for America.

I just wanted to express our friendship and our faith in the United States. What happened today in Washington, D.C., is not America, definitely. We believe in the strength of our democracy. We believe in the strength of American democracy.

Chancellor Angela Merkel of Germany on Thursday condemned the mob violence at the U.S. Capitol and blamed the chaos on the rhetoric of President Trump, as leaders around the world expressed concern about the health of American democracy.

Ms. Merkel said she deeply regretted that Mr. Trump had not accepted his defeat in the election and again on Wednesday failed to accept its outcome. “He stoked uncertainties about the election outcome, and that created an atmosphere that made the events of last night possible,” she said.

Ms. Merkel, who addressed a joint session of Congress during a visit to Washington in 2009, said it was “tragic” that people lost their lives during Wednesday’s violence but that it was a sign of “hope” that Congress worked through the night. A woman was fatally shot inside the Capitol and three other deaths were reported nearby, the police said.

Ms. Merkel’s comments mirrored a deep-seated faith in the strength of democracy in the United States that is held by many in Europe.

President Emmanuel Macron of France, in a formal address recalling longstanding ties between his country and the United States, said the chaos in Washington did not reflect the America he knew.

“We believe in the strength of our democracies,” Mr. Macron said. “We believe in the strength of American democracy.”

Le Monde, one of France’s leading newspapers, said in an editorial on Thursday that the violence in Washington amounted to a “day of shame.”

In the first government response from Russia, the spokeswoman for the country’s foreign ministry, Maria Zakharova, said, “We once again point out that the electoral system in the United States is archaic and doesn’t meet modern standards of democracy, creating the possibility for multiple violations and the American media have become instruments of political struggle.”

Ms. Zakharova said she hoped the “friendly people of America will with dignity get through this dramatic period in their own history.”

Russian politicians and political analysts were quick to point out that the attack on the Capitol would send immediate ripples through one cornerstone of U.S. foreign policy: support for pro-Western protesters in the street politics of Eastern Europe and the former Soviet Union.

“Color revolutions just lost a serious argument in their favor,” Konstantin F. Zatulin, deputy chairman of a committee in Russia’s Parliament on relations with former Soviet states, said in an interview, referring to American-supported popular uprisings in countries including Georgia, Serbia and Ukraine over the past two decades.

In Asia, much of which was asleep while U.S. lawmakers were being evacuated from the Capitol, the unsettling scenes from Washington greeted those who were starting their day.

In China, a spokeswoman for the Ministry of Foreign Affairs, Hua Chunying, pointedly referred to American expressions of support for the huge protests that took place in Hong Kong, which at one point included the takeover of the legislature in 2019.

“You may still remember that at the time, American officials, congressmen and some media — what phrases did they use for Hong Kong?” she said in Beijing on Thursday. “What phrases are they using for America now?”

Prime Minister Jacinda Ardern of New Zealand said she and her country were “devastated” by the events in the United States, but she expressed confidence that democracy would ultimately prevail.

“The right of people to exercise a vote, have their voice heard and then have that decision upheld peacefully should never be undone by a mob,” she wrote on Twitter.

Charles Santiago, an opposition lawmaker in Malaysia, said that Mr. Trump had joined other world leaders “in subverting democracy and the will of the people.” He cited Prime Minister Hun Sen of Cambodia and President Rodrigo Duterte of the Philippines.

“The U.S. has lost its moral authority to preach democracy and human rights to other countries,” he said. “It has become part of the problem.”

Call them rioters. Or armed insurrectionists. But Erica de Bruin, a political scientist who literally wrote the book on how to prevent coups, said she would not call it a coup.

“I don’t object to anyone wanting to use the term ‘coup’ at this point,” she said in an interview. “The word coup conveys seriousness, and I don’t want to police the language of politicians or activists or those trying to oppose Trump’s actions. But I don’t think we’re there yet.”

The crucial factor, she said, is that a coup attempt requires force or the threat of force from an organized armed group, usually, though not necessarily, a military. And while many in the violent mob of President Trump’s supporters that stormed the Capitol building on Wednesday were armed, they did not appear to be part of any organized paramilitary organization.

Naunihal Singh, a professor at the Naval War College whose research focuses on coups, said he did not think this was a coup because President Trump encouraged the insurrectionists in his capacity as head of their movement, but did not do so via the powers of the president. “We can deal with this sort of power grab far more easily than one which uses presidential authority, if we’re willing to treat him the same way we would treat any regular citizen doing the same,” he said. (Dr. Singh spoke in his personal capacity.)

The scenes at the Capitol bear an obvious resemblance to coups, which often involve an armed takeover of legislative buildings. But the resemblance, Dr. de Bruin said, is a superficial one.

“They’re emulating coup plotters,” she said. “But when coup plotters do that, it’s because they think that occupying that position makes them look like they are holding political power. No one thinks that this group is actually in control.”

Both experts, however, cautioned against concluding that this is not a serious threat to American democracy.

“Coups aren’t that common these days,” Dr. de Bruin said. “The way we tend to see democracies fail these days is through this subtle undermining and chipping away of democracy.”

Representative Jake LaTurner, Republican of Kansas, announced that he received a positive test result for the coronavirus on Wednesday night, after he spent the day participating in a failed effort to stop Congress from formally certifying President-elect Joseph R. Biden Jr.’s victory.

Mr. LaTurner, a first-term lawmaker who assumed office this month, took the test as part of travel guidelines from the District of Columbia that require visitors to be tested, according to a message from his Twitter account posted early Thursday. He was not experiencing any symptoms.

As a group of Trump supporters, many without masks, stormed the Capitol on Wednesday, members of Congress and their staffers crowded together to hide from the violence and chaos that unfolded. Senators were rushed in close quarters to safety through the Capitol tunnels.

Coronavirus cases in the United States on Wednesday continued to rise, with 255,730 daily cases and nearly 4,000 deaths reported. It was the country’s worst day of the pandemic so far, in both categories, though reporting delays over the holidays may have affected the totals.

Congress has come under fire for lacking consistent procedures to protect members and staff from the coronavirus. More than 100 members of Congress have either tested positive, quarantined or come into contact with someone who had the virus, according to GovTrack.

Mr. LaTurner does not plan to return to the House floor for votes until he is cleared to do so, a message from his Twitter account said.

Anyone traveling to Washington from a district with more than 10 coronavirus cases per 100,000 people must get a test within 72 hours of traveling, and visitors to the city must be tested within three to five days of arrival.

The U.S. Office of Government Ethics published financial disclosure forms on Thursday morning for Katherine Tai, the Biden administration’s expected nominee for the position of United States Trade Representative. Thai currently serves as chief trade counsel for the House Ways and Means Committee.

The forms show Ms. Tai’s assets are far more limited than many of the outgoing members of the Trump administration, like Wilbur Ross, the wealthy financier who serves as commerce secretary, and Ms. Tai’s predecessor as trade representative, Robert E. Lighthizer.

Ms. Tai has retirement accounts valued between $70,000 and $350,000, and other investment accounts valued between $425,000 and $1,050,000. She also owns residential real estate in San Francisco valued between $500,000 and $1 million, and has bank accounts with between $350,000 and $750,000 in cash.

But Ms. Tai also has liabilities, namely three mortgages of between $1 million and $2 million, according to the filing.

WASHINGTON — The White House has so far declined to ask for the resignations of its ambassadors and other political appointees, potentially delaying a turnover of the government’s most senior officials and risking more chaos across the federal work force in President Trump’s final days in office.

Mr. Trump’s refusal to issue an order for those letters of resignation — which has been a routine proceeding in past administrations — is another snub of presidential decorum that broadcasts the depths of division inside the United States, even as Mr. Trump promised early Thursday to ensure an “orderly transition” to the administration of President-elect Joseph R. Biden Jr. after an assault by Trump supporters on the Capitol.

The White House did not respond on Thursday morning to the latest of several requests for comment about when it would formally call for resignations.

The delay has irritated some foreign allies who want to plan for Mr. Biden’s policies but are awaiting the departure of Mr. Trump’s ambassadors so that career diplomats at American embassies are not put in the position of being insubordinate to their bosses. More broadly, without a clear directive to leave, officials said, some political appointees may burrow into the federal bureaucracy until Mr. Biden forces them out.

“There’s been no memo sent to anybody,” said Christopher R. Hill, who was an ambassador to four countries under Presidents Bill Clinton, George W. Bush and Barack Obama and also served as an assistant secretary of state to Mr. Bush. “And so a number of ambassadors are saying, ‘Hey, I’ll just stay until I’m informed otherwise.’”

Mr. Hill predicted, though, that the delay would not dramatically undercut national security or foreign policy.

For more than 30 years, since at least the end of the Reagan administration, outgoing presidents have requested the resignations of political appointees, who account for about 4,000 of the federal government’s 2.1 million employees. Their timely departure helps prevent a personnel bottleneck immediately after the inauguration that would occur if departing employees were still being processed just as new appointees were coming in.

House Democrats on Thursday announced the start of a “robust” investigation into the law enforcement breakdown that allowed a violent mob of Trump supporters to storm the Capitol as lawmakers were formalizing the victory of President-elect Joseph R. Biden Jr.

“It is obvious that there was a severe systemic failure in securing the building’s perimeter and in the response once the building was breached,” Representatives Rosa DeLauro, Democrat of Connecticut and chairwoman of the Appropriations Committee, and Tim Ryan, Democrat of Ohio, said in a statement.

While they stressed that the responsibility for the violence rested with President Trump and his supporters, they said “the breach of the Capitol raises serious questions about what law enforcement did and what they should have done differently.”

The Appropriations Committee funded the Capitol Police at more than $515 million for the 2021 fiscal year, which began on Oct. 1. That is similar to what Baltimore spends on policing and more than Detroit and Atlanta spend on law enforcement.

Mr. Ryan is chairman of an appropriations subcommittee that has jurisdiction over the budget for the Capitol Police. That subcommittee will lead the investigation, which he said would include “hearings to directly question key leaders about what went wrong.”

“To ensure the safety of those who work and visit here, we must get to the bottom of these breakdowns and prevent them from ever happening again,” the Democrats wrote.