WASHINGTON (Reuters) - An interview of U.S. President Donald Trump by special counsel Robert Mueller was less likely after this week’s FBI raids on Trump’s personal lawyer, two people familiar with the matter said on Thursday.

Special Counsel Robert Mueller departs after briefing members of the U.S. Senate on his investigation into potential collusion between Russia and the Trump campaign on Capitol Hill in Washington, U.S., June 21, 2017. REUTERS/Joshua Roberts

Trump was infuriated by Federal Bureau of Investigation raids on Monday on the New York law office and home of Michael Cohen, which followed a referral by Mueller.

Still, the president’s tendency to change his mind added to uncertainty about whether an interview would ultimately take place.

In a tweet early on Thursday, Trump said that he backed a “cooperative” approach to Mueller’s investigation of possible collusion between Moscow and Trump’s presidential campaign.

“I have agreed with the historically cooperative, disciplined approach that we have engaged in with Robert Mueller,” Trump said on Twitter.

Further suggesting that tensions could blow over, a third source familiar with the matter said the relationship with Mueller remained strong and constructive and discussions were expected to recommence soon.

Russia has denied U.S. intelligence agencies’ findings that it interfered in the 2016 campaign to try to tilt the vote in Trump’s favor. Trump has denied any collusion and has repeatedly attacked Mueller’s investigation as a politically motivated “witch hunt.”

Trump’s outburst after the FBI searches raised concerns among critics and lawmakers, including some in Trump’s own Republican Party, that he might try to have Mueller removed.

The president denied a New York Times report on Tuesday that he had sought to fire Mueller in December. “If I wanted to fire Robert Mueller in December, as reported by the Failing New York Times, I would have fired him,” he said on Twitter early on Thursday.

White House lawyers Ty Cobb and Donald McGahn have told Trump that firing Mueller would leave him vulnerable to charges of obstruction of justice, two officials told Reuters on Tuesday. They said Trump must have “good cause” to order the Justice Department official overseeing the Russia probe, Deputy Attorney General Rod Rosenstein, to oust Mueller.

ADVICE FROM FORMER AIDE

One of the sources familiar with the matter and another person said on Thursday that Rosenstein is on shaky ground. The second person said the feeling among White House and Justice Department officials was that Rosenstein was abdicating authority and not putting constraints on the investigation.

Rosenstein was at the White House on Thursday discussing the status of congressional requests, another of the sources said.

Steve Bannon, a former senior adviser to Trump, has encouraged White House aides to advise Trump to fire Rosenstein, the Washington Post reported on Wednesday, citing unidentified sources. It also said Bannon wanted the White House to stop cooperating with the Mueller investigation and fire Cobb.

Cobb, the lawyer in charge of the White House response to the Russia investigation, has stressed cooperation with Mueller. The White House has said it has turned over tens of thousands of pages of documents to the special counsel’s team.

Trump said in one of his Twitter messages on Thursday that he had full confidence in Cobb.

A bipartisan group of senators put forward legislation on Wednesday to protect Mueller and his investigation, which the Senate Judiciary Committee is expected to consider next week.

If passed, the legislation would allow the special counsel to be fired only “for good cause” by a senior Justice Department official, with a reason given in writing; provide recourse if the special counsel was fired without good cause; and preserve the staffing and materials of a pending investigation.

“Anyone advising the President - in public or over the airwaves - to fire Bob Mueller does not have the President or the nation’s best interest at heart. Full stop,” Republican Senator Orrin Hatch wrote on Twitter on Thursday.