He added that the focus of the investigation remained “the nursing homes, the allegations of sexual harassment and the bridge,” referring to claims of a cover-up of potential structural problems on a major new bridge, named for Mr. Cuomo’s father, that crosses the Hudson River.
The testing program was overseen by senior health officials who often sent staff — outfitted in full protective garb, including face shields and scrubs — to do in-home tests. Mr. Cuomo requested the tests for his family, according to one of the people with knowledge of the effort.
On Thursday, a spokesman for Mr. Cuomo, Richard Azzopardi, reiterated that the administration was rejecting “insincere, hypocritical efforts to rewrite the past.”
“In the early days of this pandemic, when there was a heavy emphasis on contact tracing, we were absolutely going above and beyond to get people tested,” Mr. Azzopardi said, saying that the effort included “in some instances going to people’s homes” to identify cases and prevent others from developing the disease.
“Among those we assisted were members of the general public, Democratic and Republican legislators, and reporters — including local and national reporters — state workers and their families, and those believed would be in direct contact with the governor,” he said.
Indeed, top state officials working on the pandemic response also received priority testing, including Patrick J. Foye, the chairman of the Metropolitan Transportation Authority, and Rick Cotton, the head of the Port Authority of New York and New Jersey, both of whom tested positive.
Mr. Cotton, who is 76 and a longtime close ally of Mr. Cuomo’s, said on Thursday that he “reached out” to the state Health Department and arranged tests for himself and his wife, Elizabeth Smith, the chief executive of the Central Park Conservancy, after she “became ill and began exhibiting symptoms.”