Rosenstein testified before the Senate Judiciary Committee on Tuesday that he has no reason to believe the special counsel has been compromised and no reason to remove Mueller. In an interview on CNN's "New Day", Ruddy said, "I think it is a consideration the President has had because Mueller is illegitimate as special counsel".
Mueller was succeeded by James Comey, who was sacked by Trump last month while he was overseeing the investigation into potential Russian interference into last year's election and potential collusion with the Trump presidential campaign.
A long-time friend of Mr Donald Trump has said that the US President was considering whether to fire Mr Robert Mueller, the special counsel investigating possible ties between Mr Trump's election campaign and Russian officials.
"I am thrilled to have a chance to help you to live up to your campaign promises", said Commerce Secretary Wilbur Ross. But both appearances, however, are being overshadowed by Sessions' public appearance at a Senate intelligence committee hearing. Ruddy had not met directly with the President while he was there.
"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.
Spokeswoman Sarah Huckabee Sanders told reporters aboard Air Force One that "while the president has the right to" fire Robert Mueller, "he has no intention to do so". Attorney General Jeff Sessions also made false statements under oath regarding his meetings with Russian Ambassador Sergey Kislyak, senior adviser Jared Kushner case is not looking better. "I think it is", Ruddy said.
House Speaker Paul Ryan told reporters that any talk about Mr Trump wanting to rid himself of the special investigator amounts to rumour.
"So we're getting echoes of Richard Nixon in the Saturday Night Massacre where they would have to go deep into the Justice Department to find someone who would do such a pernicious and despicable act of firing Mueller", he continued. The attorney general is expected to be closely questioned about his contacts with Kislyak and his role in last month's firing Federal Bureau of Investigation director James Comey.
Rosenstein said the attorney general would be the only one who could fire Mueller.
"In this kind of environment, I don't give the benefit of the doubt to somebody who can only hire Democrats, but claims that we ought to trust him", Gingrich said during a previous interview on "CBS This Morning". An order from the president would not necessarily qualify, he said. Trump could alternatively direct the Justice Department to repeal the regulation, potentially allowing the president to directly fire a special counsel.
Ruddy lashed out at Spicer and the White House communications team in a Tuesday interview on MSNBC, calling their behavior "amateur hour" and accusing them of failing the president.
That pushback came from top officials from the party's congressional wing, as well as from administration officials who actually have the legal authority over the special counsel and would need to be involved in any firing.
Rosenstein noted that he is the only one who could fire Mueller, as Attorney General Jeff Sessions has recused himself from the Russian Federation investigation.