President Trump in April on Air Force One, where he was asked specifically whether he knew about the payment to a pornographic film actress, Stephanie Clifford. Mr. Trump said, “No,” and referred questions to his personal lawyer.

WASHINGTON — President Trump reimbursed Michael D. Cohen, his longtime personal lawyer, for a $130,000 payment that Mr. Cohen has said he made to keep a pornographic film actress from going public before the 2016 election with her story about an affair with Mr. Trump, according to Rudolph W. Giuliani, one of the president’s lawyers.

That statement, which Mr. Giuliani made Wednesday night on Fox News, contradicted the president, who has said he had no knowledge about any payment to the actress, Stephanie Clifford, to keep quiet before the election.

Asked specifically last month by reporters aboard Air Force One whether he knew about the payment, Mr. Trump said, “No,” and referred questions to Mr. Cohen. He was then asked, “Do you know where he got the money to make that payment?”

“No,” Mr. Trump responded. “I don’t know.”

In an interview with The New York Times shortly after his Fox News appearance, Mr. Giuliani said that he had documentation showing that Mr. Trump had personally made the payments, and he indicated that the goal was to conclusively demonstrate that there was no campaign finance violation involved.

“That removes the campaign finance violation, and we have all the documentary proof for it,” Mr. Giuliani said. He added that when the initial payment was made, Mr. Cohen did it “on his own authority.”

“Some time after the campaign is over, they set up a reimbursement, $35,000 a month, out of his personal family account,” Mr. Giuliani said, adding that over all, Mr. Cohen was paid $460,000 or $470,000 from Mr. Trump through those payments, including for “incidental expenses” that he had incurred on Mr. Trump’s behalf.

Mr. Giuliani said that he had spoken with the president before and after his interview on Fox News, and that Mr. Trump and other lawyers on the team were aware of what he would say.

Ms. Clifford, whose stage name is Stormy Daniels, outside federal court last month in New York. Mr. Giuliani’s statement appears to contradict the president, who has at times said that he was unaware of the payment to Ms. Clifford.

The president has repeatedly denied that he had an affair with Ms. Clifford, who has described having intimate contact with Mr. Trump before he became president.

Mr. Giuliani’s comments are also in direct contrast to what Mr. Cohen has been saying for months — that he used his own money to pay Ms. Clifford, whose stage name is Stormy Daniels. Mr. Cohen is under investigation by the F.B.I., which raided his home and office last month and seized documents that included information about the payments to Ms. Clifford.

“They funneled through a law firm, and the president repaid it,” Mr. Giuliani told Sean Hannity, the Fox News host. After Mr. Hannity asked for clarification, Mr. Giuliani insisted: “That was money that was paid by his lawyer. The president reimbursed that over the period of several months.”

The source of the $130,000 payment…