Prominent Republicans nationwide reveled in the news. Donald Trump Jr. mockingly shared several old tweets from the attorney general, in which he had denounced the president and expressed solidarity with victims of sexual assault; “This didn’t age well,” he wrote. Kellyanne Conway, the president’s counselor, wrote in a tweet that Mr. Schneiderman had been “drunk with power.” By early Tuesday, the president had not commented on Mr. Schneiderman’s resignation.

Mr. Schneiderman’s fellow Democrats had also called on him to step aside, with Mr. Cuomo, Senator Kirsten Gillibrand and Mr. Heastie saying the attorney general was incapable of continuing in his office.

And people in both parties were quick to point out that some right-wing pundits who blasted the attorney general were also staunch defenders of President Trump, who has himself been accused of a slew of sexual abuse.

While Mr. Schneiderman’s resignation signals the probable end of a career that many had seen as gaining quick national prominence, the legal fallout is most likely only beginning.

A spokesman for Cyrus R. Vance Jr., the Manhattan district attorney, said Mr. Vance’s office had opened an investigation into the allegations in the New Yorker article. Mr. Schneiderman had, at the direction of Mr. Cuomo, himself been probing Mr. Vance’s office over questions about its handling of groping allegations against the film mogul Harvey Weinstein in 2015. A spokeswoman for the attorney general’s office did not immediately comment on whether that review would continue.

Separately, Mr. Cuomo also said on Monday that he would direct an “appropriate New York district attorney” to investigate the allegations. An administration official said Monday that the governor’s office wanted to avoid any conflict of interest and ensure the proper jurisdiction, given the attorney general’s review of Mr. Vance and the fact that some of the alleged abuse occurred on Long Island.

Mr. Schneiderman had been in contact with a criminal defense lawyer late Monday afternoon to advise him on his response to The New Yorker, according to two people with knowledge of the matter. Later, an associate of Mr. Schneiderman was looking for a lawyer to represent him in connection with the criminal investigation, several other people with knowledge of the matter said.