Because Sessions had recused himself from the Russia investigation over his connection to Trump's campaign and his undisclosed meetings with the Russian ambassador, it was Rosenstein's decision to appoint a special counsel to lead the investigation.
"I think that he should be more cognizant of making sure that the people who come to work with him are non-partisan, for his own credibility", Bennett said of Mueller.
Republicans in Congress are also shaking off the notion that Trump could fire Mueller.
The White House pushed back, but only hours after the claim had been parsed and dissed with warnings about how it would only make things worse for Trump, who chose to ignore it all together in a series of tweets on Tuesday morning, and seemed more focussed on a fresh setback to his travel ban.
Rumors that Trump was considering firing Mueller - whom the Justice Department appointed to investigate allegations that Trump's presidential campaign may have coordinated with Russian Federation - emerged Monday afternoon in a Washington version of the game Telephone. Justice Department regulations specify that a special counsel can only be removed for "misconduct, dereliction of duty, incapacity, conflict of interest, or for other good cause", and that the "specific reason" must be spelled out in writing.
House Speaker Paul Ryan says the White House and President Donald Trump should let the special counsel's investigation continue, and await vindication.
Criticism of special counsel Robert Mueller used to be off limits.
Super Mario Odyssey producer explains possession mechanic — Mad hatter
Special pixelated pipes turn Mario into 8-bit graffiti on the wall to let him run a challenge in traditional 2D platforming style. It's weird, right? With Cappy , Mario can possess and control everything from a Bullet Bill to ... well, a dinosaur.
The news comes one day after Rosenstein affirmed his support for the special counsel, despite recent reports that Trump was weighing Mueller's dismissal.
Rosenstein said "no, I have not", when asked by Sen. "If there were not good cause, it would not matter to me what anybody said", he said.
"First, most simply, Trump could order Mueller fired", Katyal said.
The new talk about dismissing Mueller appeared to be coming from Trump allies - including some close to White House strategist Steve Bannon - who are increasingly frustrated with the prospect of a long and winding probe.
Jack Goldsmith, a Harvard Law professor who headed the Justice Department's Office of Legal Counsel during the George W. Bush administration, offered a careful assessment of the consequences of a Mueller firing early Tuesday on the Lawfare blog. Comey said he and other Federal Bureau of Investigation officials expected Sessions to recuse himself before it was publicly announced but would not discuss why they came to that conclusion.
"Director Mueller is going to have the full degree of independence that he needs to conduct that investigation appropriately", Rosenstein said.
On Tuesday, Attorney General Jeff Sessions told the Senate intelligence committee that there were discussions at high levels about firing FBI Director James Comey even before Sessions was confirmed.
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