US President Donald Trump has denied a report on Friday that he ordered the firing of Special Counsel Robert Mueller last June, calling it "fake news".

The New York Times reported yesterday that Mr Trump backed down from his order after the White House counsel threatened to resign rather than follow his directive, citing four people told of the matter.

"Fake news, folks, fake news," Mr Trump told reporters in the Swiss ski resort of Davos, when asked about the report.

According to the media reports Mr Trump backed down after the White House counsel threatened to resign rather than follow his directive.

Mr Mueller, who is investigating allegations of Russian meddling in the 2016 US election, learned of the incident in recent months as his investigators interviewed current and former senior White House officials in an inquiry into whether the president obstructed justice, the Times reported.

Amid media reports that Mr Mueller was looking into a possible obstruction case, Mr Trump argued that the former Federal Bureau of Investigation director had three conflicts of interest that disqualified him from overseeing the probe, two of the people said, according to the Times report.

First, Mr Trump said that a past dispute over fees at Trump National Golf Club in Sterling, Virginia, had led Mr Mueller to resign his membership, the newspaper reported.

The president also said Mr Mueller could not be impartial because he had most recently worked for a law firm that previously represented the president’s son-in-law, Jared Kushner.

Mr Trump also said Mr Mueller had been interviewed to return as the director of the Federal Bureau of Investigation the day before he was appointed special counsel in May, the Times reported, citing the two people.

White House counsel Donald McGahn said he would quit rather than follow through on the order to fire Mr Mueller, the Times reported, citing the people.

Mr McGahn disagreed with the president’s case for dismissing Mr Mueller and told senior White House officials that firing him would have a catastrophic effect on Mr Trump’s presidency and raise questions about whether the White House was trying to obstruct the Russia probe, according to the people cited by the Times.

Mr McGahn also told White House officials that Mr Trump would not follow through on the dismissal on his own, and the president then backed off his demand, according to the people, who the Times said spoke on condition of anonymity because they did not want to be identified discussing a continuing investigation.

Mr Mueller was appointed special counsel in May by the Justice Department after Mr Trump fired FBI Director James Comey, who was leading the agency's Russia investigation.

Russia has denied any meddling and Mr Trump has denied any collusion.

Mr Comey's firing is central to whether Mr Trump may have committed obstruction of justice.

Mr Trump said on Wednesday he would be willing to be interviewed under oath by Mr Mueller, and according to sources with knowledge of the investigation, Mr Trump's attorneys have been talking to Mr Mueller's team about an interview.