As the facts around a payment to adult film actress Stormy Daniels continue to evolve, comments made this week by US President Donald Trump’s new lawyer may have given investigators more leads, not less.

Mr Trump and the White House previously denied the president paid $US130,000 ($173,000) in hush money to the actress (real name Stephanie Clifford) in the days leading up to the election for her silence over an alleged affair in 2006.

But in an interview that caught White House staff unawares, Mr Trump’s new lawyer and former New York mayor Rudolph Giuliani on Wednesday broke ranks and said the president reimbursed his long-time personal lawyer Michael Cohen for the payment.

“Imagine if that came out on October 15, 2016, in the middle of the last debate with Hillary Clinton,” Mr Giuliani said. “Cohen didn’t even ask. Cohen made it go away. He did his job.”

Stormy Daniels says she had a sexual encounter with Donald Trump in 2006.

According to the Washington Post, this crucially establishes intent – an important aspect in some crimes – and suggests the payment was made to protect the Trump campaign.

In that case, the payment would have been a campaign contribution which would have to be publicly reported and above the the legal limit of $US2700 ($3580) that Mr Cohen could have given, making it a campaign finance violation.

The president was in damage control on Friday as Mr Giuliani released a statement backtracking on his previous comments.

Mr Trump undercut his new lawyer and told reporters that Mr Giuliani would eventually “get his facts straight”.

“Virtually everything said has been said incorrectly, and it’s been said wrong, or it’s been covered wrong by the press,” Mr Trump said.

“He is a great guy,” he said of Mr Giuliani before incorrectly telling reporters he joined his legal team “a day ago” when he started a month ago.

“He’ll get his facts straight.”

In a statement, Mr Giuliani tried to clarify the confusion, saying that his “references to timing were not describing my understanding of the president’s knowledge, but instead, my understanding of these matters.”

Legal experts told the Washington Post that Mr Giuliani’s comments may help investigators established campaign finance violations, which can be difficult to prove.

The Manhattan office, home and hotel room of Mr Cohen were raided by the FBI in April in connection to the payment made to Ms Clifford.

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. These agreements are…..

— Donald J. Trump (@realDonaldTrump) May 3, 2018

…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,……

— Donald J. Trump (@realDonaldTrump) May 3, 2018

…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.

— Donald J. Trump (@realDonaldTrump) May 3, 2018

Investigators are exploring whether Mr Cohen committed any crimes by regularly paying hush money to stop damaging stories from Mr Trump appearing when he was a candidate.

Mr Trump was forced to concede the money came out of a monthly retainer he paid Mr Cohen but denied it was related to his campaign.

The agreement was used to stop the false and extortionist accusations made by her about an affair,” he tweeted. “This was a private agreement. Money from the campaign, or campaign contributions, played no roll in this transaction.”

Mr Trump’s and Mr Cohen’s lawyers believe the investigation is largely aimed at pressuring Mr Cohen to cooperate with the special counsel investigation, people familiar with their discussions told the Washington Post.

Mr Trump has described the raids as “a witch hunt”.

Ebony Bowden contributed reporting from New York City.