WASHINGTON (TNS) — Despite new protestations from the White House that President Donald Trump does not plan to fire Robert Mueller, two leading Republican senators Sunday called for a law to protect the special counsel leading the Russia investigation.

"I've got legislation protecting Mr. Mueller, and I'll be glad to pass it tomorrow," Sen. Lindsey Graham, R-S.C., said on ABC's "This Week."

"Mr. Mueller is the perfect guy to get to the bottom of all this, and he will," he said.

Graham also appeared to brush aside the White House campaign to dismiss the investigation as politically motivated and the president's denial that he tried to fire Mueller last year, as was reported by the New York Times and subsequently confirmed by other news organizations.

"We're not going to say it's fake news and move on," Graham said.

Sen. Susan Collins of Maine, another prominent Republican, said she had faith in Deputy Attorney Rod Rosenstein, to whom the special counsel reports and who would have to sign off on any attempt to dismiss him.

But she said on CNN's "State of the Union" that it "certainly wouldn't hurt" to pass a bill that would block Trump from firing Mueller.

Collins, who sits on the Senate Intelligence Committee, also said that in her opinion, Trump, who has prolifically posted on Twitter about the investigation for months, should "never" talk about it except in private with legal counsel.

Both bills put forward in the Senate to protect Mueller are bipartisan. Graham's version was proposed with Sen. Cory Booker, D-N.J. A similar proposal is co-sponsored by Sens. Thom Tillis, R-N.C., and Chris Coons, D-Del.

But Republican leaders have called attempts to prevent the president from trying to derail the investigation unnecessary.

House Majority Leader Kevin McCarthy, R-Calif., repeated that view Sunday. On NBC's "Meet the Press," he said, "I don't think there's a need for legislation right now to protect Mueller."

McCarthy said Trump and his staff had "fully cooperated" with the investigation. "I think we'll just continue this investigation to see where it goes," he said.

McCarthy said he had confidence in Mueller, but said there are "questions about others within the FBI" and the Justice Department, echoing allegations by other Trump allies.

A senior White House aide, meanwhile, sought to cast new doubt on reports that Trump tried to fire Mueller but was stopped by White House counsel Donald McGahn.

"I'm not aware the president ever intimated he wanted to fire Robert Mueller," legislative director Marc Short said on "Fox News Sunday."

"Robert Mueller is still the special counsel; Don McGahn is still head of White House counsel; the White House continues to cooperate in every manner, providing every document the special counsel has asked for," Short said. But he conceded that "the president has been frustrated by this investigation."

Trump has consistently denied any collusion between his campaign and the Russian government, and he said last week he is willing to be interviewed by Mueller, although his lawyers quickly interceded to say that the details were still being worked out.

One prominent former official warned against making assumptions about Mueller's ultimate findings. Interviewed on NBC, former Defense Secretary and CIA Director Robert Gates said he had "total confidence" in Mueller, a federal law enforcement veteran.

But, Gates said, "People need to be prepared that a guy like Bob Mueller may come to a different conclusion that will elate some people and anger some people."