FILE - In this Jan. 23, 2018, file photo, Sen. Susan Collins, R-Maine, speaks during a TV news interview on Capitol Hill in Washington. Collins on Sunday, Jan. 28, said President Donald Trump would be "best served" by keeping a public silence on an independent investigation into his 2016 campaign's contacts with Russia in the wake of news reports of attempted presidential interference and urged special counsel Robert Mueller to review whether Trump tried to fire him. (AP Photo/J. Scott Applewhite, File)

FILE - In this Jan. 23, 2018, file photo, Sen. Susan Collins, R-Maine, speaks during a TV news interview on Capitol Hill in Washington. Collins on Sunday, Jan. 28, said President Donald Trump would be "best served" by keeping a public silence on an independent investigation into his 2016 campaign's contacts with Russia in the wake of news reports of attempted presidential interference and urged special counsel Robert Mueller to review whether Trump tried to fire him. (AP Photo/J. Scott Applewhite, File)

WASHINGTON (AP) — Two Republican senators said Sunday that President Donald Trump would be wise to keep a public silence on an independent investigation into his 2016 campaign’s contacts with Russia in the wake of news reports that he sought to fire the special counsel.

The senators, Lindsey Graham of South Carolina and Susan Collins of Maine, also urged special counsel Robert Mueller to review whether Trump tried to fire him last June, an accusation the president has labeled “fake news.”

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“Mueller is the best person to look at it,” said Graham, describing the allegation as grave if proved true. “I’m sure that there will be an investigation around whether or not President Trump did try to fire Mr. Mueller.”

Graham, co-sponsor of legislation that would protect Mueller from being fired without a legal basis, said he would be “glad to pass it tomorrow.” But he insisted that Mueller’s job appeared to be in no immediate danger, pointing to the political costs if Trump did remove him.

“It’s pretty clear to me that everybody in the White House knows it would be the end of President Trump’s presidency if he fired Mr. Mueller,” he said.

Collins said it would certainly “not hurt” for Congress to approve added protections for Mueller given the recent media reports. But she didn’t offer a timeline.

“I think the president would be best served by never discussing the investigation, ever, whether in tweets, except in private conversations with his attorney,” she said.

The New York Times and other outlets reported that Trump backed off his attempt to fire Mueller last June only after White House lawyer Don McGahn refused to relay his directive to the Justice Department and threatened to quit if Trump pressed the issue.

According to the reports, Trump argued that Mueller could not be fair because of a dispute over golf club fees that he said Mueller owed at a Trump golf club in Sterling, Virginia. The president also believed Mueller had a conflict of interest because he worked for the same law firm that was representing Trump’s son-in-law and adviser, Jared Kushner.

On Sunday, lawmakers praised Mueller’s impartiality and expressed confidence that he would be able to conduct a full, wide-ranging investigation.

“I have complete confidence in Mr. Mueller,” Graham said. “I haven’t yet seen any evidence of collusion between President Trump and the Russians, but the investigation needs to go forward without political interference, and I’m sure it will.”

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Senate Democratic leader Chuck Schumer indicated that Democrats would try to add legislation to protect Mueller as part of an upcoming spending bill.

“The most important thing Congress can do right now is to ensure that special counsel Mueller’s investigation continues uninterrupted and unimpeded,” the New York senator said in a statement Sunday. “No one - whether it be Administration officials, Republicans or the president himself - should get in the way and undermine the investigation, and so Democrats will seek to add protections for Mueller in the ongoing budget negotiations.”

Defending the president, White House legislative director Marc Short said he didn’t know if Trump would sign legislation that would make it harder to fire Mueller. But Short stressed that despite media reports, he was not aware of any conversation in which Trump expressed a desire to fire Mueller.

“I know that the president has been frustrated by this investigation,” Short said. “He feels like there’s been millions of dollars of taxpayers’ dollars spent and no evidence yet of collusion. ...The White House continues to cooperate in every manner providing any document the special counsel has asked for.”

Short added that Trump favors releasing a classified memo produced by the House Intelligence Committee that Republicans say alleges FBI misconduct. Trump’s position is in contrast to that of the Justice Department, which has warned that the memo’s public release could be “extraordinarily reckless” and has asked to review it.

Some lawmakers said the memo’s review instead should be done by impartial third parties “outside of the Republican-led Congress.”

“I want somebody who is without a political bias to come in and look at the allegations that I have seen,” Graham said.

Graham spoke on ABC’s “This Week,” Collins appeared on CNN’s “State of the Union” and CBS’ “Face the Nation,” and Short was on “Fox News Sunday” and CBS.

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Associated Press writer Ken Thomas contributed to this report.