Mueller was appointed by the Justice Department to helm the investigation after Trump abruptly fired Comey - who was the one previously leading the Russian Federation probe - in early May. He added that no such reason now exists.
Conservative commentator Ann Coulter offered a similar message, tweeting, "Now that we know TRUMP IS NOT UNDER INVESTIGATION, Sessions should take it back & fire Mueller".
Trump refused to respond to a reporter asking four times Tuesday whether he will fire Mueller, potentially trying to create some suspense. "I think he's weighing that option".
"Let Robert Mueller do his job", Ryan said.
In a Tuesday morning Senate appropriations subcommittee hearing, Deputy Attorney General Rod Rosenstein confirmed that only he could dismiss Mueller, and even then only for a documented cause.
As expectations mounted about the upcoming open hearing of attorney general Jeff Sessions on Capitol Hill, a friend of the president added a new twist to the Russian Federation controversy by suggesting Donald Trump might be considering dismissing the special counsel investigating it. "I'm not going to follow any orders unless I believe they are lawful" and that "it wouldn't matter what anybody said".
Rosenstein assured Feinstein the firing of Mueller would not occur without his assent.
"It's a mistake to pretend that this is going to be some neutral investigation", Gingrich said.
Rosenstein's testimony before the Senate Appropriations Committee occurred just hours before Sessions was to testify in a public hearing before another Senate panel about his contacts with Russian Ambassador Sergey Kislyak and his involvement in the firing of another Federal Bureau of Investigation chief, James Comey.
Landmark success of China's quantum experiment is far-reaching
The result is an outstanding landmark in the human history of communication and physical science , and reaches far and more. Now, a new study shows a successful transmission of the entangled photons between suborbital space and Earth.
Pakistan ready to 'change history' against India
India also won the Sultan Azlan Shah Cup match against Pakistan by a convincing 5-1 margin. Sarfraz Ahmed, the captain of the Pakistan became the latest victim of the same.
Crude oil supply growth to outpace rise in consumption in 2018 - IEA
He said at OPEC's meeting in late May that there would be a "marked" decrease in the kingdom's shipments to the U.S. Crude stocks at the Cushing, Okla., delivery hub fell by 1.2 million bbl, EIA said.
Trump has made it clear that he is frustrated by the U.S. probe of Russian interference in the presidential election, which United States intelligence officials said was done to tilt the outcome in Trump's favor. "Ruddy has told friends that he went public with the Mueller story, in part, to prevent Mr. Trump from making a rash decision".
Comey also said the Federal Bureau of Investigation had "additional facts" about Sessions that he could "not discuss in an open setting".
The White House downplayed Ruddy's comments. "This clown over here, Mueller, thinks he can tell you what to do".
In 1973 President Richard Nixon ordered his attorney general to fire Archibald Cox, the special prosecutor who was leading the Watergate investigation.
The White House dismissed Ruddy's comments - but not by saying Mueller is safe. But the president and his aides have not definitively said so.
"Well, I respect the move, but the entire thing has been a witch hunt".
White House officials said late Monday that Ruddy was at the White House that day, but said he hadn't meet with the president and never spoke with him about the issue.
Trump fired Comey last month.
Barry Bennett, a GOP strategist who served as an adviser to Trump's campaign, said he believed it would be too damaging for Trump to try to remove Mueller, but that he had concerns about the appearance that the probe was being politicized.