GOP Sen. Lindsey Graham (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.

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 (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 (R-N.C.) and Christopher Coons (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.