Speaking on the Senate floor, Senator Mark Warner said the Special Counsel's investigation into alleged links between the Republican's presidential campaign and Russian meddling in last year's election must be "able to go on unimpeded."
He denounced "a growing chorus of voices in Congress, the media, and the White House" who he accused of "pushing a coordinated narrative undermining the credibility of the Special Counsel’s investigation and the FBI itself".
Republican lawmakers have seized on anti-Trump texts by an FBI agent who was involved in the Russia probe as evidence of bias in Mr Mueller's team. The Special Counsel removed the agent from his team after messages describing the President as an "idiot" and "loathsome human" came to light.
Republicans on several House of Representatives committees have also announced their own probes into long-standing political grievances, including the FBI's handling of defeated Presidential candidate Hillary Clinton's use of a private email server when she was Secretary of State.
Mr Trump has insisted he was not considering firing Mr Mueller, despite increasing attacks on the lawyer from the President's allies.
But Virginia Senator Mr Warner, vice-chairman of the Intelligence Committee, warned "the President’s track record on this front is a source of concern". He added he was "certain many of my colleagues believed that he wouldn’t possibly fire" James Comey, who was sacked as FBI director by Mr Trump in May during the investigation of former national security adviser Michael Flynn.
"Over the last several weeks, a growing chorus of irresponsible voices have called for President Trump to shut down Special Counsel Mueller's investigation," said Mr Warner, adding that the attacks were "seemingly coordinated."
"Firing Mr Mueller or any other of the top brass involved in this investigation would not only call into question this administration's commitment to the truth, but also to our most basic concept of rule of law," he added. "It also has the potential to provoke a constitutional crisis."
The senator called on Congress to make it clear to the President that firing Mr Mueller would have "immediate and significant consequences."
He added pardoning key witnesses in the probe and sacking other FBI or Department of Justice officials involved in the investigators were "red lines" that "we simply cannot allow.. to be crossed". Mr Trump has refused to say if he will pardon Mr Flynn, who has admitted lying to the FBI.
"Any of these actions would be a gross abuse of power and a flagrant violation of executive branch responsibilities and authorities," Mr Warner said.
House Democrats had circulated rumours last week that Mr Trump would fire Mueller this Friday, just before the Christmas holiday.
White House lawyer Ty Cobb said in a statement on Wednesday that the administration "willingly affirms yet again, as it has every day this week, there is no consideration being given to the termination of the special counsel".
He added: "If the media is going to continue to ask for responses to every absurd and baseless rumour, attention-seeking partisans will continue to spread them."
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