Sen. Thom Tillis (R-N.C.) said on Tuesday that he wants the Judiciary Committee to vote on his bill limiting President Trump's ability to fire Bob Mueller, but downplayed the idea that his push is a reaction to Trump's latest attack on the special counsel.

"I think it's a good bill that has enduring value beyond this presidency," Tillis told reporters.

"I do think it's a bill that's worthy of a markup in Judiciary and sending it to the floor."

He added he would be asking for the committee vote even if Hillary Clinton were in the White House and "we were having the same discussion with a different sort of a flare to it."

Tillis and Sen. Christopher Coons (D-Del.) introduced legislation last year that would let Mueller or any special counsel challenge their firing in court.

A separate bill, from GOP Sen. Lindsey Graham (S.C.) and Democratic Sen. Cory Booker (N.J.), would require a judge to approve a Justice Department request to fire Mueller or any other special counsel.

Tillis noted that he's had conversations with Graham about merging their legislation. GOP leadership has repeatedly dismissed the need for Congress to preemptively take action.

Tillis's comments come after Trump lashed out following an FBI raid on the offices and hotel room of his personal attorney, Michael Cohen. A referral from Mueller's team reportedly prompted the raid.

"Attorney-client privilege is dead!" Trump said in a tweet, adding: "A TOTAL WITCH HUNT!!!"

The president's comments sparked the latest round of warnings from Capitol Hill that firing Mueller would be a mistake.

Tillis said on Tuesday that the president appeared "frustrated" but signaled Trump had made similar comments in the past.

"I feel like the reaction we're seeing is similar to the last time he expressed frustration back in August," the North Carolina Republican said.