His impassioned response came after Senate Democrats raised questions about whether Sessions privately met with Sergey Kislyak at an April 2016 foreign policy event at the Mayflower Hotel in Washington.
President Trump has railed against the Russian Federation investigation, describing it as a "witch hunt".
Comey testified to the Senate Intelligence Committee last week that he leaked information from memos he wrote describing his private conversations with Trump. "That witness is the attorney general of the United States".
Since being appointed special counsel in May, Mueller has built a team of formidable legal minds who've worked on everything from Watergate to Enron.
"Whoever leaked [news of the obstruction investigation] was obviously reading that he was thinking about giving Mueller the boot", an official told the Daily Beast.
Now Mr. Gingrich has been joined in this chorus by a Trump confidant and golf-buddy, the President of Newsmax, who says the President is contemplating firing Mueller.
President Donald Trump "has no intention" of firing Robert Mueller, White House spokesman Sarah Huckabee Sanders said on Tuesday, but she would not say whether the president had confidence in the special counsel in the Russian Federation probe.
"It's a mistake to pretend that this is going to be some neutral investigation", Gingrich said. Could Rosenstein's job also be in jeopardy? Still, he added, "I can't imagine that that issue is going to arise".
Under questioning from South Carolina Sen. Lindsey Graham, Rosenstein said that having given political donations is not a disqualifier. "With respect to this subject, only the President or his attorneys are authorized to comment".
Former House Speaker Newt Gingrich fanned the flames of the Mueller termination rumor in an interview Tuesday morning on CBS, saying that Trump called him Monday night and that he doesn't think the president will seek Mueller's dismissal.
The New York Times reported Tuesday that Trump was angered by reports that Mueller was close to fired FBI Director James Comey and entertained the idea of firing the special counsel. If there were good cause, I would consider it.
Rosenstein said Trump has not discussed the special counsel with him.
If questions arise about what matters Sessions should stay away from, he said, a career official in Rosenstein's office is consulted.
"I think he's considering perhaps terminating the special counsel", Christopher Ruddy said during an appearance on PBS' "NewsHour". The Times reported Trump had been bothered by conservative news reports that Mueller was close to James Comey, the Federal Bureau of Investigation director whom Trump fired in May. After responding that he had not, Rosenstein reassured Shaheen of his confidence in the process.
Ryan noted if Trump chose to fire Mueller, it would be a "big problem for him politically". He described Mueller as operating independently from the Justice Department in his investigation. Republicans and Democrats alike are calling for this investigation, for the process to continue. "But what we do know, if indeed the president does fire Mueller, it shows he's impeding the process yet again".