Asked on board Air Force One whether he knew about the payment, Trump said flatly: “No.” He also said he didn’t know why Cohen had made the payment or where he got the money.

In a phone interview with Fox and Friends last week, however, Trump appeared to muddy the waters, saying that Cohen represented him in the “crazy Stormy Daniels deal”.

Trump tried to clarify the matter on Thursday in a series of tweets.

“Mr. Cohen, an attorney, received a monthly retainer, not from the campaign and having nothing to do with the campaign, from which he entered into, through reimbursement, a private contract between two parties, known as a non-disclosure agreement, or NDA,” Trump wrote on Twitter.

“These agreements are very common among celebrities and people of wealth. In this case it is in full force and effect and will be used in Arbitration for damages against Ms. Clifford (Daniels). The agreement was used to stop the false and extortionist accusations made by her about an affair, despite already having signed a detailed letter admitting that there was no affair.

“Prior to its violation by Ms. Clifford and her attorney, this was a private agreement. Money from the campaign, or campaign contributions, played no roll in this transaction,” Trump concluded.

The White House referred questions to the president’s personal legal team.

Giuliani, who joined Trump’s legal team last month, said the president had repaid Cohen over several months, indicating the payments continued through at least the presidential transition, and possibly into his presidency. He also said the payment “is going to turn out to be perfectly legal” because “that money was not campaign money”.

No debt to Cohen is listed on Trump’s personal financial disclosure form, which was certified on June 16, 2017.

Giuliani also described the payment to Daniels as “a very regular thing for lawyers to do.”

Daniels’ lawyer, Michael Avenatti, called the comment “a stunning revelation”.

“Mr Trump evidently has participated in a felony and there must be serious consequences for his conduct and his lies and deception to the American people,” he said.

Giuliani made the statements to Fox host Sean Hannity, who has his own connection to the case. It was recently revealed in court that Hannity is also one of Cohen’s clients. Hannity has described his personal dealings with Cohen as mainly real estate advice and said it “never rose to any level that I needed to tell anyone that I was asking him questions”.

Daniels, whose legal name is Stephanie Clifford, says she had sex with Trump in 2006, months after his third wife gave birth to his youngest child, and was paid to keep quiet as part of a nondisclosure agreement she is now seeking to invalidate. She has also filed a defamation suit against Trump after he questioned a composite sketch she released of a man she says threatened her to stay quiet.

The White House has said Trump denies having a relationship with Daniels.

Cohen had said previously: “Neither the Trump Organisation nor the Trump campaign was a party to the transaction with Ms. Clifford, and neither reimbursed me for the payment, either directly or indirectly.” He notably did not include the president personally.

Asked about Cohen’s denial, Giuliani said that he didn’t know if Cohen made the payment without asking Trump but that he had “no reason to dispute that.”

The revelation from Giuliani came as Cohen was under escalating legal pressure. He is facing a criminal investigation in New York, and FBI agents raided his home and office several weeks ago seeking records about the nondisclosure agreement.

Daniels’ lawsuit over the hush deal has been delayed, with the judge citing the criminal investigation.

The payment to Daniels has raised numerous legal questions, including whether it was an illegal campaign contribution and, now, loan.

Law firms advance expenses for clients as a matter of course, and so there’s nothing inherently improper about a lawyer covering a particular payment and then being reimbursed for it. In this case, though, the client who apparently reimbursed the expense was running for president and the money was paid just days before the election, raising questions about whether Cohen’s law practice was functioning as a vendor for the campaign and whether the expense was therefore an unreported campaign expenditure. If so, that could be legally problematic.

A key question is timing. If Cohen or Trump could establish that discussions with Daniels over the payment long predated his run for office, that could help them with the argument that the money was a personal rather than political expense.

“It obviously increases the president’s exposure to potential campaign finance violations, but it also makes him look terrible,” said Sol Wisenberg, a defence lawyer who was a deputy independent counsel during the Starr special counsel investigation into President Bill Clinton.

“I don’t understand the Giuliani strategy,” he added. “Maybe it’s been too long since he’s been in the criminal justice field.”