But a long-time friend of Mr Trump said the president was considering sacking Mr Mueller.
For now, the staff has prevailed.
Chris Ruddy, Newsmax CEO and friend to President Trump, said that he's thinking about doing something shocking - he's weighing whether to dismiss Special Counsel Mueller, who was appointed over the investigations into Russian Federation.
Dianne Feinstein, top Democrat on the Senate Judiciary Committee, said she was "increasingly concerned" that Trump will fire both Mueller and Rosenstein. Though some in the White House have preached caution, fearing a repeat of the firestorm over Comey's firing, many in Trump's orbit - including his son Donald Trump Jr. and adviser Newt Gingrich - have deemed Mueller biased and worthy of dismissal. "Can you just tell me, what is the allegation against the President or any of his officials?"
Today, Attorney General Jeff Sessions will testify in front of the Senate Intelligence Committee's open hearing on Russian Federation, to clarify amid growing criticism of Republicans after Comey´s testimony.
Justice Department Deputy Solicitor General Michael Dreeben donated in 2008 to a political action committee for then-Democratic presidential candidate Barack Obama as well as a PAC for Hillary Clinton in 2006.
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WhatsApp's end-to-end encryption, however, means that Facebook has no access to the content of most messages and it can't deploy the same image and text analysis tools.
"This is an illegitimate special counsel", Ruddy said.
Ruddy agrees that the move would be a wrong move, but dismissed the investigation Mueller is overseeing.
"I never said I spoke to the President", he added.
Barry Bennett, a GOP strategist who served as an adviser to Trump's campaign, said he believed it would be too damaging for Trump to try to remove Mueller, but that he had concerns about the appearance that the probe was being politicized. But Trump's conservative allies have begun to turn on the special counsel, despite initially praising his appointment.
Despite the speculation, Principal Deputy White House Press Secretary Sarah Huckabee Sanders told reporters Tuesday that "while the president has the right to [fire Mueller], he has no intention to do so".
The two men worked closely together in the aftermath of the September 11, 2001, attacks when Mueller was Federal Bureau of Investigation director and Comey was a high-ranking Justice Department official in the George W. Bush administration.
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The United Kingdom general election in 2017 took place on Thursday 8 June 2017. That's why we're ready to start very quickly. "I can't negotiate with myself".
In a post of his own on Tuesday, The Washington Post's Philip Bump spelled out the number of steps Trump would need to take before he could fire Mueller, should he make that decision.
While the president's aides have sought to sow skepticism about Mueller, whom they interviewed about the possibility of returning to the FBI job the day before he accepted his position as special counsel, few have advocated his termination, reflecting the recognition that Trump's angry reactions to the congressional and FBI investigations now underway are imperiling his presidency. He made the comments after being seen leaving the White House Monday.
For all the talk of how no one in the West Wing tells the president "no", many people do - though often unsuccessfully.
They say Trump did not collude with Russian Federation and see the investigation as a politically motivated sham that handicaps Trump's ability to execute his agenda, according to one person who advises the White House on how to handle the probe.
Comey testified last week that he also felt pressured to drop the Flynn probe.
Trump obstruction charge is investigated as Texas Tribune polls released
As Mueller assembles his investigative team, statements by Trump's friend Christopher Ruddy this week set off new questions. Trump later contradicted his own staff, saying on May 11 he had the Russian Federation issue in mind when he fired Mr.
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