The White House distanced Trump from Ruddy but did not deny that Trump is considering such a move.
On CNN to anchor Chris Cuomo: "I think it is a consideration the president has had, because Mueller is illegitimate as special counsel. With respect to this subject, only the President or his attorneys are authorized to comment".
Rosenstein is scheduled to testify today before both Senate and House subcommittees regarding the Justice Department's budget, and he is likely to be questioned about Mueller's status.
According to Ruddy, Mueller was a candidate to replace James Comey as Federal Bureau of Investigation director and had met privately with Trump on that subject.
Former House Speaker Newt Gingrich fanned the flames of the Mueller termination rumor in an interviewTuesday morning on CBS, saying that Trump called him Monday night and that he doesn't think the president will seek Mueller's dismissal.
But expressions of discontent with Mueller are bubbling up nonetheless.
- Jeannie Rhee contributed $16,450 to Democrats from 2008 to 2016.
If true, that would make sense ... but Trump should tread carefully here. She asked whether he has seen "any evidence of good cause" to fire Mueller.
The top Justice Department official overseeing the investigation into Russian Federation also assured senators that Mueller has been granted complete independence to do his work.
Peter Carr, a spokesman for Mueller, declined to comment on Ruddy's remarks.
Rosenstein appointed Mueller last month to lead the investigation into Russian meddling in last year's election and potential Trump campaign ties to that effort.
Anxiety about the probe - and fresh concerns about the political leanings of some of the attorneys involved - is percolating in the West Wing of the White House.
Ruddy said in an interview Monday with Judy Woodruff of PBS, "I think he's weighing that option".
The notion was dismissed by senior White House aides later Monday evening, who said that Ruddy does not speak for the president.
Given that kind of support, a Democratic lawmaker, Ted Lieu, taunted the White House over the Mueller-firing chatter: "Double dare exists. I have confidence in Bob Mueller".
In Mueller's case, Trump would have to ask Rosenstein to do the firing. The person spoke on condition of anonymity to discuss private conversations. But Gingrich said that Mueller will only "annoy" but not "get Trump".
Gingrich is correct that there is a certain partisan tilt to the team of top-notch investigators being assembled by the ex-FBI director: Jeannie Rhee, Michael Dreeben, Andrew Weissmann and James Quarles are renowned in their fields and have made repeated donations to Democrats. With the concept of irony safely strangled, Trump's zany outburst of praise for his own presidency was greeted with somber affinity. US Justice Department regulations outline that a special counsel can be fired by the US attorney general "for cause". Trump decided he had to fire Flynn on February 13, saying even as he did so that Flynn had done nothing wrong and shouldn't be punished.
Former Speaker of the House Newt Gingrich said Tuesday on ABC's "Good Morning America" that while he feels "independent counsels are very unsafe", he doesn't think Trump should force Mueller out.
Added Collins: It would "certainly be an extraordinarily unwise move".
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