US president Donald Trump has suggested Rudy Giuliani, the aggressive new face of his legal team, needs to "get his facts straight" about the hush money paid to porn actress Stormy Daniels just before the 2016 election.

Former New York City mayor Mr Giuliani quickly came up with a new version of events after Mr Trump's intervention.

The president chided Mr Giuliani even as he insisted that "we're not changing any stories" about the $130,000 settlement, which was paid to Ms Daniels to keep her quiet about her allegations of an affair with Mr Trump.

Hours later, Mr Giuliani backed away from his previous suggestion that the October 27 settlement had been made because Mr Trump was in a critical phase of his campaign.

"The payment was made to resolve a personal and false allegation in order to protect the president's family," Mr Giuliani said in a statement released on Friday.

"It would have been done in any event, whether he was a candidate or not."

A day earlier, Mr Giuliani had said on Fox News: "Imagine if that came out on October 15, 2016, in the middle of the last debate with Hillary Clinton."

Mr Trump said that Mr Giuliani was "a great guy but he just started a day ago", and the former mayor of New York City was still "learning the subject matter".

Mr Giuliani revealed this week that Mr Trump knew about the payment to Ms Daniels made by his personal lawyer, Michael Cohen, and the president had paid Mr Cohen back.

Mr Giuliani insisted the president did not know the specifics of Mr Cohen's arrangement with Ms Daniels until recently, telling Fox & Friends on Thursday that the president did not know all the details until "maybe 10 days ago".

He told The New York Times that Mr Trump had repaid Mr Cohen $35,000 a month "out of his personal family account" after the campaign was over.

He said Mr Cohen received $460,000 or $470,000 in all for expenses related to Mr Trump.

Mr Giuliani's suggestion that the president knew anything about the payments - even as a monthly retainer - appeared to contradict Mr Trump, who has repeatedly denied the affair and told reporters on Air Force One last month that he had not known about any settlement with Ms Daniels.

Mr Trump's irritation was plain when reporters reminded him of his previous denial. He blasted the media for focusing on "crap" stories like the Daniels matter and special counsel Robert Mueller's probe over Russian meddling in the 2016 election.

The president claimed "virtually everything" reported about the payments - which are the subject of legal action and media attention - has been wrong, but he declined to elaborate.

It was Mr Trump's own team's missteps that yielded another day of headlines about Ms Daniels. In his statement, Mr Giuliani said his previous "references to timing were not describing my understanding of the president's knowledge, but instead, my understanding of these matters".

Mr Giuliani's statement correcting himself came just a day after he said: "You won't see daylight between me and the president."