While Mr. Schneiderman’s resignation signals the probable end of a career that many had seen as gaining quick national prominence — he had emerged as something of a liberal darling, filing more than 100 legal or administrative actions against the Trump administration and congressional Republicans — 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 he would direct a district attorney, or possibly multiple, to investigate the allegations, which took place in a number of counties and thus could fall under multiple jurisdictions.

“I want to make sure the district attorneys have no conflicts whatsoever with the attorney general’s office, either institutionally or personally,” he said. When asked if Mr. Vance should recuse himself, Mr. Cuomo said “it’s an issue that we have to look at.”

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.

Mr. Schneiderman has denied wrongdoing, describing the acts as part of consensual relationships.

Several women’s groups that had previously supported Mr. Schneiderman — he was known for being an outspoken advocate for women’s advancement, especially for reproductive rights — expressed shock and sorrow. The National Institute for Reproductive Health, which had honored the attorney general at a May 1 luncheon, said in a statement that it was “appalled and horrified.” (By Tuesday, the group had removed Mr. Schneiderman from its list of honorees.) Sonia Ossorio, president of New York’s arm of the National Organization for Women, which endorsed Mr. Schneiderman in his 2010 and 2014 campaigns, said she was “in shock.”

“I’m just beside myself right now,” she said.