Though the story has evolved over the last few days, Mr. Trump has said that "very strong recommendation from the Deputy Attorney General" played a role in his decision to terminate Comey.
Mr Mueller, who is a widely respected figure who enjoys bipartisan support, will have sweeping powers and the authority to prosecute any crimes he might uncover.
Panel Chairman Richard Burr and Vice Chairman Mark Warner said they will schedule the hearing for after Memorial Day. But was Rosenstein also aware of why Trump meant to dismiss Comey?
A number of lawmakers exited the meeting stressing that Mueller's probe, while appropriately diving in to all possible Trump-Russia ties, may make it more hard for current congressional investigations to access vital intelligence.
He criticized Comey's testimony to Congress - "a poor, poor performance" - and said that helped seal his fate. It immediately escalated the legal stakes - and the potential political damage - for a president who has tried to dismiss the matter as partisan witch hunt and a "hoax".
That revelation came after almost the entire complement of the U.S. Senate attended a briefing with Deputy Attorney General Rod Rosenstein in a secure auditorium beneath the Capitol.
Mr Comey was abruptly fired last week, in a move that shocked Washington.
But Rosenstein's unwillingness to answer substantive questions frustrated some senators. Sen.
Comey, like most modern Federal Bureau of Investigation heads, had looked to keep the White House at arm's length but his involvement in investigating Democratic candidate Hillary Clinton during the campaign made him wary of appearing to be too close to the new administration. His drafting of a memo criticizing Comey's handling of the Clinton email investigation-which the administration now admits is an entirely pretextual basis for the dismissal of the FBI Director-struck Ben as shocking for reasons he explained.
Mueller's appointment was not expected to affect the FBI or congressional investigations.
Massachusetts Democratic congressman Seth Moulton says Rosenstein didn't "do a lot to bolster our confidence in him". It says the president then told Russia's foreign minister and ambassador that he "faced great pressure because of Russian Federation". "It's going to hamper our ability to get to the bottom of this quickly, I believe". He was so valued that President Barack Obama asked him to stay on two years longer than his 10-year term.
That's because Comey, as FBI director, was leading the Russia investigation and had recently announced the probe was targeting alleged Russian ties to Trump's campaign. Rosenstein then wrote the above-mentioned memo to Attorney General Sessions regarding Comey's conduct, and he notes that he "chose the issues to include" himself.
"Comey was disgusted. He regarded the episode as a physical attempt to show closeness and warmth in a fashion calculated to compromise him before Democrats who already mistrusted him".
Trump is leaving Friday for his first foreign trip, to the Mideast and beyond, and aides had hoped the disarray at home would have been calmed if not resolved by take-off time.
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