"I will tell you my own view is it is entirely possible for a president to obstruct justice. If a president committed perjury to lie to or mislead investigators, if he encouraged others [to], if he destroyed evidence," Toomey said.

While the Pennsylvania senator declined to comment directly on the recent letter from Trump's lawyers, he added that he could think "of lots of ways a president could obstruct justice."

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Senators were quizzed on the issue after The New York Times reported that Trump's lawyers sent a letter to special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE in January arguing the president could not have obstructed justice because he has constitutional authority over all federal investigations.

The letter argues that the Constitution gives Trump the broad authority to, "if he wished, terminate the inquiry, or even exercise his power to pardon."

Other Republican senators noted that the Senate previously tried to convict President Clinton of obstruction of justice as part of his impeachment trial.

"I've always said I didn't think anybody is above or below the law," Shelby added.

Shelby is one of several GOP senators still in office who voted in 1999 that Clinton was guilty of obstructing justice.

Several other now-sitting GOP senators were members of the House during the Clinton impeachment scandal.

"Well you can be impeached for obstructing justice, that's what we did with Clinton. Whether or not he can be charged criminally, while he's in office? I don't know," he said.

Asked if he would advise Trump against obstructing justice, Graham said: "Number one, I advise everybody from president to the people operating the elevator, don't obstruct justice."

The January letter to Mueller was authored by John Dowd, one of Trump's former lawyers, and Jay Sekulow, another one of Trump's lawyers.

Trump's lawyer Rudy Giuliani was not a part of his legal team when the letter was sent but argued over the weekend that Trump has the ability to pardon himself, while predicting he wouldn't.

GOP senators on Monday stopped short of saying Trump doesn't have the legal ability to use his presidential powers to protect himself, but warned that doing so would spark a political firestorm.

Trump has increasingly lashed out at Mueller's probe into Russia's interference in the 2016 presidential election, including potential collusion between the Trump campaign and Moscow.

"The appointment of the Special Counsel is totally UNCONSTITUTIONAL! Despite that, we play the game because I, unlike the Democrats, have done nothing wrong!" Trump said in a tweet on Monday morning.