Washington (AFP) - US President Donald Trump insisted Sunday there was no shortage of lawyers willing to help him fight a collusion investigation as two more attorneys decided against joining his defense team.

Days after the resignation of John Dowd as Trump's lead attorney in the handling of allegations of collusion with Russia, US media reported that Joe diGenova and his wife and colleague Victoria Toensig had reversed a decision to come on board.

"The President is disappointed that conflicts prevent Joe diGenova and Victoria Toensing from joining his Special Counsel legal team," Jay Sekulow, another of Trump's lawyers, was quoted as saying in a statement.

The White House had announced last week that DiGenova -- who is a familiar figure on US news networks -- had been hired to bolster the legal team tasked with responding to special counsel Robert Mueller's investigation into last the 2016 US election.

His hiring came amid reports that another high-profile attorney Theodore B. Olson -- who served as solicitor general under former president George W. Bush -- had turned down an invitation to sign up with the Trump team.

Writing on Twitter on Sunday, Trump denounced any suggestion that he was struggling to attract top legal talent as "fake news."

"Many lawyers and top law firms want to represent me in the Russia case...don't believe the Fake News narrative that it is hard to find a lawyer who wants to take this on," the president wrote.

"Fame & fortune will NEVER be turned down by a lawyer, though some are conflicted.

"Problem is that a new lawyer or law firm will take months to get up to speed (if for no other reason than they can bill more), which is unfair to our great country -- and I am very happy with my existing team."

Dowd quit days after Trump directly attacked former FBI chief Robert Mueller's sprawling Russia investigation as a "witch hunt," raising fresh questions about whether the president was interfering with the probe.

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Mueller is expected to seek to interview the president over allegations that his campaign team colluded with Russia during the 2016 presidential election and that Trump himself may have obstructed the investigation.

Trump said on Thursday that he was still willing to be interviewed by Mueller.

The increasingly embattled Trump is also fighting off allegations that he had an affair with the porn star Stormy Daniels, with his defense by his long-time personal lawyer Michael Cohen.