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.

[Read what Mr. Giuliani said here.]

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, the former New York mayor and longtime Trump confidant who recently joined the president’s legal team, said that he had documentation showing that Mr. Trump had personally made the payment. Mr. Giuliani indicated that the goal was to conclusively demonstrate that there was no campaign finance violation involved.