In yet another turn in a legal battle that has plagued President Trump for months, Michael D. Cohen, his longtime fixer, offered late Friday night to tear up a nondisclosure agreement with a pornographic film star who has long claimed she had an affair with Mr. Trump.

It remained unclear why Mr. Cohen made the abrupt move to scrap the hush-money deal with the star, Stephanie Clifford, who is better known as Stormy Daniels. But one effect of voiding the arrangement would be that it could spare Mr. Trump the embarrassment of having to give a deposition in a lawsuit related to the case.

In a letter dated Sept. 7, Mr. Cohen’s lawyer, Brent H. Blakely, wrote to Ms. Clifford’s lawyer, Michael Avenatti, saying that Mr. Cohen had agreed “to accept the rescission” of the deal, which was reached in October 2016, a month before the presidential election.

Under the terms of the arrangement, Essential Consultants LLC, a shell company Mr. Cohen created, paid Ms. Clifford $130,000 not to speak publicly about a sexual relationship she said she began with Mr. Trump in 2006 after they met at a celebrity golf tournament in Nevada.