After Mr Giuliani’s comments the president confirmed on Twitter that Mr Cohen had been “reimbursed” for making a “non-disclosure agreement” with Ms Daniels.
Such agreements were “very common among celebrities and people of wealth,” he added.
Mr Trump said that “money from the campaign, or campaign contributions, played no roll in this transaction”.
Mr Giuliani said: “It wasn’t true (the affair). However, imagine if that came out on October 15, 2016, in the middle of the last debate with Hillary Clinton. Cohen didn’t even ask (Mr Trump). Cohen made it go away. Cohen thought $130,000 was cheap. He did his job.”
He said the repayment by Mr Trump “removes the campaign finance violation. Some time after the campaign is over they set up a reimbursement, $35,000 a month, out of his (Mr Trump’s) personal family account”.
Mr Giuliani added that Mr Trump was “probably not aware” of the payment to Ms Daniels at the time as he had given Mr Cohen “discretion to solve” such matters, and did not know all the details until “maybe 10 days ago”.
Michael Avenatti, Ms Daniels’ lawyer, said: “We predicted months ago that it would be proven that the American people had been lied to about the $130,000 payment and what Mr Trump knew, when he knew it, and what he did in connection with it.