Sen. Thom Tillis Thomas (Thom) Roland TillisWhat Senate Republicans have said about election-year Supreme Court vacancies Chamber of Commerce endorses McSally for reelection Airline job cuts loom in battleground states MORE (R-N.C.) on Sunday defended the bill he introduced last week that would let any special counsel challenge their firing in court.

"This is very important," he said during an interview on "Fox News Sunday." "It's an important part of what we need to do to re-establish the public trust in the Department of Justice."

Tillis was pressed on whether President Trump factored into the legislation.

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"There's no question ... because clearly, the date that we've made the bill retroactive to," he said.

"But this is about the Department of Justice. This is about my confidence in the attorney general and my confidence in the Department of Justice to move forward in an appropriate manner."

Tillis said he doesn't want to restrict the authority of the administration or the Department of Justice to remove a special counsel.

"We just want to make sure to the American people they can be convinced it was done for the right reasons," he said.

Tillis also said he doesn't believe the probe into Russian election meddling and possible ties between the Trump campaign and Moscow is a "witch hunt."

"I think that this is just a way to put this behind us," he said, adding that he wants remove the distractions so he can continue to support Trump's agenda.

Tillis and Sen. Christopher Coons (D-Del.) last week introduced the Special Counsel Integrity Act, which would let special counsel Robert Mueller or any special counsel challenge their firing in court.

The challenge would be heard by a three-judge panel within 14 days. If they aren't able to find "good cause" for the firing, the special counsel would be reinstated.

The bill would be retroactive back to May 17, when Mueller was named as special counsel for the investigation into Russia's election interference, but would also apply to any special counsel named after that date.

Coons in a separate interview early Sunday touted the legislation, adding that Congress could possibly hire Mueller if Trump fired the special counsel amid his ongoing Russia probe for the Justice Department.

"I think if the president should fire Robert Mueller abruptly, that would be crossing a big line," Coons told ABC's "This Week." "And I think you would see strong bipartisan action from the Senate, which might include our reinstating him or our rehiring him to continue to conduct that investigation on behalf of Congress."

--Olivia Beavers contributed to this report, which was updated at 10:34 a.m.