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President Trump told top officials this past June that he wanted to fire special counsel Robert Mueller, but was talked out of doing so by White House counsel Don McGahn and other aides, a source close to the White House told Fox News late Thursday.

The source could neither confirm nor deny a New York Times report that Trump ordered Mueller's dismissal, but backed down when McGahn threatened to resign instead.

However, the source added that then-White House chief of staff Reince Priebus and chief strategist Steven Bannon believed last summer that Trump would fire Mueller and were very worried about the political fallout.

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"They said, 'This is going to blow up,'" the source recounted to Fox.

White House lawyer Ty Cobb declined to comment on either the source's account or the New York Times report "out of respect for the Office of the Special Counsel and its process."

According to the Times report, which cited "four people told of the matter," Trump claimed that Mueller had three conflicts of interest that disqualified him from overseeing the investigation into alleged collusion between the Trump campaign and Russian officials.

Those conflicts included the fact that Mueller had been interviewed to replace the fired James Comey as FBI Director the day before he was appointed special counsel in May. Another alleged conflict Trump cited was that Mueller had once resigned his membership at Trump National Golf Club in northern Virginia in a dispute over fees.

The Times also reported that McGahn told White House officials that Trump would not carry out Mueller's firing on his own.

The Times also reported that Trump considered firing Deputy Attorney General Rod Rosenstein and elevating Associate Attorney General Rachel Brand to oversee Mueller's investigation. The report did not say what Trump's rationale for dismissing Rosenstein would be.

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The response from Democrats was nearly immediate. Sen. Mark Warner, D-Va., vice chairman of the Senate Select Committee on Intelligence, said that if the report in The Times is true, Trump has crossed a "red line."

"Any attempt to remove the Special Counsel, pardon key witnesses or otherwise interfere in the investigation would be a gross abuse of power, and all members of Congress, from both parties, have a responsibility to our Constitution and to our country to make that clear immediately," Warner said.

Attorney General Jeff Sessions recused himself from the Russia investigation in early March after acknowledging that he had two previously undisclosed encounters with the Russian ambassador during Trump's 2016 presidential campaign.

On Wednesday, Trump told reporters that "I'd love to" talk to Mueller as part of the investigation, subject to his lawyers' approval. The president has repeatedly denied any wrongdoing and told reporters that there was "no collusion whatsoever" and "no obstruction whatsoever."

In a July interview with The New York Times, Trump warned Mueller against expanding the special counsel investigation to his family's financial affairs.

"I think that's a violation. Look, this is about Russia," said Trump, who added that Mueller had "many other conflicts" in addition to his interview to run the FBI.

Fox News' Samuel Chamberlain contributed to this report, along with The Associated Press.