Deputy Attorney General Rob Rosenstein was praised for the Mueller appointment.
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. Rosenstein last month appointed a special counsel to oversee the Russian Federation investigation.
He said he has found no good cause to fire Mueller. "You have my assurance that we are faithfully going to follow that regulation, and Director Mueller is going to have the independence he needs".
No such allegations against Trump or anyone on his staff have been made, Ruddy said.
Trump's allies have begun raising questions about special counselRobert Mueller's impartiality - he's a former FBI director who has worked with fired FBI Director James Comey - and floating the idea that Trump might replace him.
"No, I have not", Rosenstein said.
Sessions recused himself from investigations related to the Trump campaign in February, a move that also provoked Trump's ire.
"Senator, I'm not going to follow any orders unless I believe those are lawful and appropriate orders", Rosenstein said.
He said that, since his recusal, he had never been given information or details about the Russian Federation investigation.
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.
The effort to muddy the waters surrounding the investigation is coming amid growing White House concern that the probe could detract from the president's agenda for months or years to come. And Rosenstein said Mueller could not be fired without his personal assent. "I think there's a conflict there". "I don't give the benefit of the doubt to somebody who could only hire Democrats but claims we ought to trust him".
Fleischer and Gingrich had previously vouched for the character and integrity of Mueller, who was appointed Federal Bureau of Investigation director by Bush and whose term was extended an extra two years by Democratic PresidentBarack Obama.
House Speaker Paul Ryan told reporters Tuesday any talk about Trump wanting to rid himself of the special investigator amounts to "rumor".
Trump advisors and conservative pundits including Newt Gingrich and Ann Coulter have called for Mueller's removal.
Mueller's hiring was meant to ensure the probe would be conducted without interference.
But it is a line of thinking that is making its way to the president's ears. The person spoke on condition of anonymity to discuss private conversations.
"While the president has every right to" fire Mr. Mueller, "he has no intention to do so", the White House spokeswoman Sarah Huckabee Sanders told reporters late Tuesday after a day of speculation over Mr. Mueller's fate.
"Look, the president of the United States, as we all know, is a unitary executive".