“The highest levels of our state and city government were well aware of Eric Schneiderman,” he said.

Mr. Gleason refused to identify the officials, and noted that the women he represented were not among the four who came forward this week in an article in The New Yorker that prompted Mr. Schneiderman’s resignation.

A spokesman for the law firm of Clayman Rosenberg, which is representing Mr. Schneiderman, declined to comment. Lawyers for Mr. Cohen did not return a call seeking comment.

In his letter, Mr. Gleason said that after his attempts to assist the women fell on deaf ears, he decided to take their accusations against Mr. Schneiderman to Steve Dunleavy, a former columnist for The New York Post. According to the letter, Mr. Dunleavy “offered to discuss the matter with Donald Trump.”

Within a day of speaking with Mr. Dunleavy, Mr. Gleason said, he received a phone call from Mr. Cohen.

“In the conversation,” Mr. Gleason recalled, “I said, ‘Listen, I’m looking for somebody to help.’ At the time, Trump was considering running for governor. And Cohen said, ‘If Trump runs and wins, you’ll have an ally for bringing these women forward.’”

Mr. Gleason added, “I’m no fan of Michael Cohen, but he was sympathetic.”

At that point, Mr. Trump and Mr. Schneiderman were warring over Trump University in a legal battle bitter enough that Mr. Trump eventually filed a complaint against Mr. Schneiderman with New York State’s ethics watchdog agency. In the wake of the lawsuit, Mr. Trump also posted a cryptic attack on Mr. Schneiderman on Twitter, comparing him unfavorably with two other Democratic politicians felled by scandal: former Representative Anthony D. Weiner and former Gov. Eliot Spitzer.