The former New York City mayor and one time presidential candidate insisted he did not know Michael Cohen, the president’s long-time attorney and personal "fixer" had done that, nor did he rule it out.
Asked whether Mr Cohen had paid multiple women for their silence before the election, Mr Giuliani told ABC News' This Week: “I have no knowledge of that, but I would think if it was necessary, yes."
Mr Cohen has already admitted to paying $130,000 (£96,000) to Stormy Daniels, an adult film star who claims to have had an affair with the president, out of his own pocket. Mr Trump says he had no knowledge of the payment.
Playboy model Karen McDougal, have claimed Mr Cohen made similar arrangements with them.
Last month FBI agents raided Mr Cohen’s offices and hotel room last month, reportedly looking for – in part – evidence of payments to Ms Daniels, Ms McDougal, and others.
Mr Giuliani, the latest addition to Mr Trump's legal team, appeared to contradict the president's past denials about knowledge of the payment in an interview last week.
He said Mr Trump had reimbursed Mr Cohen for the payment to Ms Daniels.
Defending Mr Giuliani, Mr Trump said the lawyer would "get his facts straight".
Mr Giuliani has since tried to clarify his remarks, saying in a statement that he made mistakes regarding the payment timeline.
“I don’t know when the president learned about it,” Mr Giuliani said of the payment on Sunday. “He could have learned about it after [the election].”
Mr Giuliani said the president paid Mr Cohen a retainer fee that the attorney then used, in part, for the payment to Ms Daniels.
He suggested the president was unaware of what the money was being used for.
“I don’t think anyone believes that he knew about it at the time,” Mr Giuliani said.
Later, Mr Giuliani said he considered the $130,000 a “nuisance payment,” adding: “People don’t go away from $130,000.”
Ms Daniels, whose real name is Stephanie Clifford, has sued Mr Trump and Mr Cohen in an attempt to invalidate a non disclosure agreement she says was intended to keep her silent about their alleged affair.
Ms Daniels’ attorney, Michael Avenatti, urged the public to watch Mr Giuliani’s interview on Sunday, calling it an “unmitigated disaster”.
He tweeted: “This is what happens when you can’t keep your lies straight."
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