A lawyer for President Donald Trump arranged a $130,000 payment to a former adult-film star a month before the 2016 election as part of an agreement that precluded her from publicly discussing an alleged sexual encounter with Mr. Trump, according to people familiar with the matter.

Michael Cohen, who spent nearly a decade as a top attorney at the Trump Organization, arranged payment to the woman, Stephanie Clifford, in October 2016 after her lawyer negotiated the nondisclosure agreement with Mr. Cohen, these people said.

Ms. Clifford, whose stage name is Stormy Daniels, has privately alleged the encounter with Mr. Trump took place after they met at a July 2006 celebrity golf tournament on the shore of Lake Tahoe, these people said. Mr. Trump married Melania Trump in 2005.

After the agreement, Ms. Clifford’s camp complained the payment wasn’t being made quickly enough and threatened to cancel the deal, some of the people familiar with the matter said.

Ms. Clifford has appeared in about 150 adult films, and was considered among the industry’s biggest stars when the then-27-year-old met Mr. Trump at the American Century Championship in 2006, held at Edgewood Tahoe golf course in Nevada.

Another adult-film star, Jessica Drake, later alleged in an October 2016 news conference that Mr. Trump kissed her and two other women without permission in a hotel suite after the same 2006 golf event.

“I did not sign [a nondisclosure agreement], nor have I received any money for coming forward,” Ms. Drake said this week in an emailed statement. “I spoke out because it was the right thing to do.”