GOP Sen. Lindsey Graham Lindsey Olin GrahamSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (S.C.) and Democratic Sen. Cory Booker (N.J.) are moving to limit the Trump administration's ability to fire Robert Mueller as the latter investigates any potential ties between Russia and the Trump campaign.

The legislation would require a judge to approve a Justice Department request to fire Mueller or any other special counsel. Any appeal of that decision would go to the Supreme Court, according to the bill.

"Our bill allows judicial review of any decision to terminate a special counsel to make sure it’s done for the reasons cited in the regulation rather than political motivation. I think this will serve the country well," Graham said in a statement.

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Booker added that special counsels should never be subjected to "interference or intimidation because of where an investigation takes them."

The measure, which is also backed by Democratic Sens. Sheldon Whitehouse Sheldon WhitehouseLWCF modernization: Restoring the promise Restaurant owner defends calamari as 'bipartisan' after Democratic convention appearance Warren calls on McConnell to bring Senate back to address Postal Service MORE (R.I.) and Richard Blumenthal (Conn.), is the second bill to be introduced on Thursday aimed at blocking President Trump's ability to fire Mueller and limiting the Justice Department's ability to follow such orders.

Under the Graham-Booker bill, the Justice Department would have to start the process of trying to fire a special counsel by filing "an action" with the court and notifying both the House and Senate Judiciary committees.

The Justice Department could only remove a special counsel "after the court has issued an order finding misconduct, dereliction of duty, incapacity, conflict of interest or other good cause."

Sens. 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.) and Christopher Coons Christopher (Chris) Andrew CoonsBiden promises Democratic senators help in battleground states Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Del.) also introduced legislation earlier Thursday that would block Trump from being able to fire Mueller or any other special counsel appointed since mid-May. The Justice Department appointed Mueller to lead the investigation into Russian election interference that month.

The bills come as Trump has repeatedly lashed out against Mueller's investigation, calling it a "witch hunt." Allies of the administration have also accused the former FBI director, who is widely respected in Washington, of being too biased to lead the probe.