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

The New York Times reported on Thursday that 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," Trump told reporters in Davos, when asked about the report.

The Times cited four sources who say that's because White House lawyer Donald McGahn threatened to quit rather than fire Mueller.

Robert Mueller is special counsel investigating alleged Russian meddling in the 2016 election and the Times cites sources that say he learned of Trump's orders to fire him through his team's interviews with senior officials over whether the president obstructed justice.

The report says when Trump heard Mueller was looking into an obstruction case, the president said the ex-FBI director had three conflicts of interests disqualifying him from heading up the investigation.

First, Trump said Mueller disputed fees at the Trump National Gold Club in Virginia, which led him to resign his membership.

Second, the president said Mueller could not be impartial because he had just worked for a law firm that once represented Trump's son-in-law Jared Kushner.

Finally, Trump said Mueller had been interviewed to return as FBI director the day before he was appointed special counsel last May.

The Times' sources said McGahn disagreed with all these points he told senior officials firing Mueller would impact Trump's presidency and raise questions over whether the White House was trying to obstruct the Russia probe.

The Times' sources say it was then that Trump backed off.

Mueller was appointed special counsel by the US Justice Department after Trump fired FBI director James Comey who had been leading the agency's Russia probe.

Comey's firing is central to the question of whether Trump obstructed justice.

Trump said on Wednesday he would be willing to be questioned under oath by Mueller and sources say the president's attorneys are talking with Mueller's team about an interview.

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