He said there is no cause to consider removal, and that that the Attorney General's office alone would make that decision with the special counsel.
Sessions, who had been slated to testify before the Senate budget panel, will appear later Tuesday before the Senate Intelligence Committee investigating Russian interference in the 2016 elections.
Until now, Mueller had drawn widespread praise from Republicans and Democrats alike.
Even as leading Republican legislators Tuesday waved off the idea of firing Mueller, expressions of discontent with Mueller have bubbled up nonetheless.
White House spokeswoman Sarah Huckabee Sanders said via email, "Chris speaks for himself".
In appointing Mueller last month, Rosenstein said that the "public interest requires me to place this investigation under the authority of a person who exercises a degree of independence from the normal chain of command".
He called because "I have been very clear" about Mueller and the lawyers he's hired amounting to a "rigged game", Gingrich said in an interview Tuesday on CBS.
Peter Carr, a spokesman for Mueller, declined to comment on the issues Gingrich and others have raised.
Mueller, who preceded Comey as Federal Bureau of Investigation director, was the longest-serving director since J. Edgar Hoover.
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.
[Newsmaker] Trump decries being target of Russian Federation probe
McCabe was referring to the agency's investigation into possible collusion between the Trump campaign and Russian officials. During the meeting, the president brought up Flynn and told Comey "I hope you can let this go", according to the memo.
The claim that Trump wants to terminate Mueller, divulged by the chief executive of Newsmax Media and friend of Trump, Christopher Ruddy, was predictably accompanied by paltry bickering within the White House, as The New York Times reports.
Ruddy said Mueller's special counsel status entails a "conflict" since Trump previously spoke with Mueller about nominating him for a government position.
Still, it took until Tuesday night for the White House to actually dispute Ruddy's suspicion.
The Daily Beast reported a second senior administration official pointed to Trump's role in propagating the rumor he might fire Mueller, suggesting the leak to the Post on Wednesday might have been an unintended outcome of that move. The interview was first reported by PBS. It is unclear whether Mueller was interested in returning to that job.
They say Trump did not collude with Russian Federation and see the investigation as a politically motivated sham that handicaps Trump's ability to execute his agenda, according to one person who advises the White House on how to handle the probe. Still, Gingrich said any special counsel with an agenda can "all of the sudden find something procedural and technical to latch onto".
Trump can not directly dismiss Mueller.
"While the president has the right to, he has no intention to do so", Sanders said when asked whether Trump was considering the move.
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.
"I think Congress should now intervene and they should abolish the independent counsel", the former House speaker said. Indeed, his expectation that threatening to oust Mueller might compel him to soft-pedal the F.B.I. probe betrays a remarkable naivete of how Washington, and longtime civil servants like Mueller, operate.
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