Ruddy also claimed that Mueller interviewed with Trump as POTUS was interviewing possible Federal Bureau of Investigation director candidates, just a few days before being named special counsel by deputy Attorney General Rod Rosenstein.
As special counsel Robert Mueller builds his legal team, Mr Trump's allies have begun raising questions about the former Federal Bureau of Investigation director's impartiality, implying he can not be trusted to lead the probe.
"You're creating a debate that's not happening", said House Majority Leader Kevin McCarthy on Tuesday morning, responding to a reporter's question about the rumor. If Mr Rosenstein refused, Mr Trump could fire him, too.
Rod Rosenstein told lawmakers of a Senate appropriations subcommittee that he has seen no good cause to remove special counsel Robert Mueller from the probe.
"I think it is a consideration the President has had, because (Robert) Mueller is illegitimate as special counsel", Ruddy told CNN's Chris Cuomo on "New Day" Tuesday.
Sources told The Times that staff worked to talk Trump out of firing Mueller, what they viewed would have been a disastrous decision for the administration.
Trump told NBC's Lester Holt in an interview on May 11 days after Comey was sacked that he fired him because "this Russian Federation thing with Trump and Russian Federation is a made up story".
He said those concerns included the interview for the Federal Bureau of Investigation post and connections between Mr Mueller's law firm and White House officials. "I am confident he will have sufficient independence".
Rosenstein is charged with Mueller's fate because Attorney General Jeff Sessions recused himself from all matters having to do with the Trump-Russia investigation. Ruddy paid lip service to that being a "significant mistake", but followed immediately saying there is no justification for the special counsel.
Cosby buoyant as jury deliberates
She sued Cosby in 2005 where he testified as part of that lawsuit, he later settled the case for a sum that was undisclosed. He made some powerful statements that people either said, 'Yeah, Amen, ' or 'That's not the way we are'.
That memo detailed a February meeting in which Trump allegedly pressed Comey to drop the FBI's investigation into former national security adviser Michael Flynn. Mr Gingrich said he is troubled by Democratic donations of Mr Mueller's picks to help lead the probe.
Now, Trump could order Rosenstein to fire Mueller.
If Mr Trump instructs Mr Rosenstein to dump Mr Mueller, it would evoke memories of 1973, when two top Justice Department officials, Mr Elliott Richardson and Mr Bill Ruckelshaus, resigned rather than obey then President Richard Nixon's order to fire Mr Archibald Cox, the special prosecutor conducting the Watergate investigation.
"Look, the president of the United States, as we all know, is a unitary executive". Gingrich later clarified that the "bad people" he was referring to are the "people who are going to be after" the president.
"I never said I spoke to the President", he added.
It wasn't clear whether Ruddy, who speaks with the president often, was basing his remarks on a conversation he had had with Trump.
Under Department of Justice rules, it is actually up to the deputy attorney general to make that call, though the president could bypass that protocol.
White House press secretary Sean Spicer said Monday that Ruddy did not speak with Trump about firing Mueller as special counsel and other White House aides suggested the Newsmax CEO was only speaking for himself.
Gingrich's comments mark an apparent change of heart, as he previously tweeted his overwhelming support of Mueller, once calling him a "superb choice".
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