MOSCOW — A ninth grader in the Russian city of Yekaterinburg asked his classmates this week why it was that they did not like President Vladimir V. Putin.
According to their teacher, Irina V. Skachkova, they responded by citing the jailed opposition leader Aleksei A. Navalny: “Putin has a palace that was built with stolen money, and Putin is himself a thief.”
Mr. Navalny’s dramatic return to Russia on Sunday and his immediate arrest, followed by his release of a video documenting Mr. Putin’s purported secret palace on the Black Sea, has captivated many young Russians and prompted the authorities to scramble to keep them away from protests planned across the country on Saturday.
Ms. Skachkova, like many teachers across Russia, said she was told by her superiors to come up with counterprogramming for her students on Saturday and to plead with parents that they keep young people from taking to the streets.
“Chasing media attention, THEY are putting KIDS in DANGER!” said the message that she said she was told to send out to parents’ chat groups.
Some universities threatened students with expulsion if they were caught attending the protests calling for Mr. Navalny’s release, which are being organized in dozens of cities across Russia even though local officials have not authorized them.
The Education Ministry urged families to spend the weekend doing nonpolitical activities like “taking a walk in a park or a forest.” Russia’s telecommunications regulator said it had ordered social networks to take down posts promoting the Saturday protests, and the country’s top investigative body said it had started a criminal investigation into the alleged incitement of minors to join.
But it was far from clear that the government’s push to dissuade young people from protesting would have much of an impact — and there were indications that it has raised even more awareness about the planned demonstrations.
On YouTube, Mr. Navalny’s 113-minute-long report about Mr. Putin’s palace — which the Kremlin has denied — remained among the top trending videos in Russia for the fourth day in a row, with a total of more than 57 million views. On the social network TikTok, which is popular with young people, the hashtag dedicated to Saturday’s protests remained accessible, and videos tagged with it had been viewed more than 125 million times.
“I know for certain that there are many good people outside my prison, and that backup is on its way,” Mr. Navalny said in a message from jail that was posted on his Instagram page on Friday.
Mr. Navalny’s supporters say the scale of Saturday’s protests will be crucial in determining his fate. The 44-year-old opposition leader fell into a coma after a near-fatal poisoning in Siberia last August and was airlifted to Germany for treatment. Western officials say he was poisoned by a military-grade nerve agent in an assassination attempt by the Russian state.
Russian authorities denied the assertion and promised to arrest Mr. Navalny if he returned to Russia for violating the parole terms of a suspended sentence he received in 2014.
Nevertheless, Mr. Navalny flew home to Moscow on Sunday, and as expected, he was detained at passport control. He now faces a prison sentence — and his supporters say that only street protests can deter the Kremlin from locking him up for years.
Dmitri S. Peskov, the Kremlin press secretary, told reporters Friday that it was “unacceptable” that unauthorized street protests were being planned and that “young people, kids and so on” were being invited to take part. Mr. Navalny’s supporters said they were not specifically calling on children to join the protests.
Ahead of the protests, the police have also detained Mr. Navalny’s supporters across Russia. Kira Yarmysh, Mr. Navalny’s press secretary, was ordered jailed for nine days on Friday.
But the seemingly Sisyphean scramble by the Russian authorities to get social networks to remove pro-Navalny content highlighted what is increasingly emerging as a major vulnerability for the Kremlin: the availability of low-cost, high-speed, mostly uncensored internet access in almost every populated corner of the country’s 11 time zones.
The government has tried and largely failed to rein in the internet. Last year, for example, it dropped a two-year-long effort to block the messaging network Telegram, a ban that users quickly found ways to circumvent.
On Friday, Russia’s telecommunications regulator, Roskomnadzor, said that YouTube, Instagram and the Russian social network VKontakte had begun following an order from Russia’s prosecutor-general that they remove “calls for children to participate in illegal mass events.” The social networks did not immediately respond to requests for comment.
But the biggest problem, the regulator said, was TikTok, the Chinese-owned app that hosts seconds-long viral videos, often musically themed. Videos marked with the #Navalny hashtag on the network had been viewed more than 800 million times by Friday.
In one clip “liked” more than 500,000 times, a young woman who provides pithy English lessons offered tips on how to sound like an American — “I’m gonna call my lawyer!” — if detained at the protests.
“The highest level of activity continues on the social network,” Roskomnadzor said in a statement, referring to TikTok. “New appeals are appearing, in some cases being disseminated in an artificial manner.”
The regulator said TikTok had removed 38 percent of illegal content. TikTok did not respond to a request for comment.
Across the country, according to local news media reports, schools and universities were scheduling exams or festivities on Saturday to prevent students from attending. A state university in the city of Kostroma north of Moscow warned students that by participating in protests, “you will destroy your reputation and cast a shadow on your university.”
That prompted outraged responses on social media and, according to one student, only served to encourage others to consider attending.
“I know people who didn’t plan on going anywhere, and then when they heard about these bans, they decided to find out what it was they were being prohibited from doing and then said they wanted to participate in the protests,” said Kirill Prokofiev, a master’s student in history.