But Ruddy opened a new line of questions about Mueller's impartiality - the fact that Trump had considered Mueller for the Federal Bureau of Investigation director's job before he was named special counsel.
The president has railed against the Russian Federation investigation, which was taken over by Justice Department special counsel Robert Mueller last month, as a "witch hunt". This would coincide with the many news stories and opinions from Trump supporters discrediting Mueller despite their approval of his appointment by Rosenstein.
The president's personal friend, Newsmax CEO Chris Ruddy said late Monday that Trump was considering terminating Mueller.
"I think the best advice is to let Robert Mueller do his job", Ryan told reporters Tuesday after a closed-door meeting with House Republicans. All of the Big Three Networks (ABC, CBS, and NBC) pushed the rumor despite the fact that their source admits he never spoke with the President and thinks he wouldn't do it.
"He didn't recall this, but I responded to his comment by agreeing that the Federal Bureau of Investigation and Department of Justice needed to be careful to follow department policy regarding appropriate contacts with the White House", Sessions said.
Justice Department spokesman Ian Prior declined to comment on the possibility of Trump seeking to remove Mueller.
While the president is deeply suspicious of Mueller, his anger is reserved for Sessions for recusing himself from the Russian Federation probe, and for Comey.
Trump, angered by reports in Breitbart News and other conservative news media that Mueller was close to James Comey, the FBI director he had fired, repeatedly brought up the political and legal implications of firing someone he viewed as incapable of an impartial investigation.
Mueller was already granted a waiver by the Justice Department to lead the probe despite a possible conflict of interest stemming from his law firm's representation of some of the people caught up in the investigation, including former Trump campaign manager Paul Manafort and Jared Kushner, the president's son-in-law and senior adviser. Under the regulation, Special Counsel Mueller may be fired only for good cause, and I am required to put that cause in writing. In his testimony to the Senate last week, James Comey made clear why he didn't want to accede to Trump's request to publicize that fact: because there was a less than zero chance that the president might become a target in the future-and then the Federal Bureau of Investigation would have to make the fact public.
Top House GOP leaders appeared frustrated at the news conference about the multiple questions about Mueller's probe and what might happen if he were forced out of his position.
Schiff told MSNBC's "Morning Joe" that if Trump fired Mueller, Congress might name its own independent counsel to investigate the case.
Rosenstein said the attorney general would be the only one who could fire Mueller.
A writer on the legal blog Lawfare said the president could even argue that the counsel is impeding his constitutional power over foreign affairs. "And when asked I said that to the president".
But the White House has now admitted there were no tapes of their conversations after all. Ruddy did not immediately respond to questions seeking clarification.
White House spokesperson Sean Spicer did not outright discount the notion of removing the special counsel, but he noted Ruddy was not a spokesperson for Trump and he had not met the President during his visit to the White House on Monday.
Christopher Ruddy, chief executive of conservative group Newsmax Media, Mr Ruddy was at the White House on Monday, but United States media reported that he did not meet Mr Trump while there.