Later Tuesday, Mr. Freidman texted a New York Times reporter about the article that had been published about his guilty plea, calling it “shameful” and comparing it to a tabloid story. “Michael is dear dear personal friend and a passive client! That’s it!” he wrote. “I am humbled and shamed!” he said, adding that the guilty plea represented “me taking responsibility for my actions.”

“I had been an officer of the court in excess of 20 years and now I am a felon!” he wrote. “I hate that I have been grouped in this runaway train that I am not a part of!”

But asked if he was cooperating with the authorities, Mr. Freidman would not respond.

After Mr. Freidman’s guilty plea, his lawyer, Patrick J. Egan of Fox Rothschild, declined to comment. But earlier this year he said his client “considers Michael a very good friend and a great client.”

Nonetheless, Mr. Freidman’s agreement to cooperate in his tax fraud case in Albany could have larger implications. Mr. Cohen is facing an investigation by the United States attorney’s office in Manhattan, which is examining his business practices. Anything that bolsters that inquiry could increase pressure on Mr. Cohen to cooperate with Robert S. Mueller III, the special counsel who is investigating the 2016 election that led to Mr. Trump’s victory.

Last month, federal agents carried out search warrants at Mr. Cohen’s home, his office and a hotel room where he was staying. The search sought a wide range of materials, including documents related to his business associates and accountants, as well as a $130,000 payment to Stephanie Clifford, the adult film actress known as Stormy Daniels, who has said she had an affair with Mr. Trump.

Mr. Cohen is best known as Mr. Trump’s personal lawyer, a role given more prominence by the actor Ben Stiller’s recurring portrayal of him on “Saturday Night Live.” But he has a wide range of business interests of his own that have drawn scrutiny, from taxicabs to real estate to a failed casino boat.