Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) on Sunday urged Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) to bring legislation that would protect 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 up for a vote.

"[McConnell's] the majority leader, not me. But if it were up to me we’d be voting on the bill and see where the votes are at," Graham said on NBC's "Meet the Press."

The South Carolina senator said there's "no indication" that President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE or acting Attorney General Matthew Whitaker are going to interfere with the special counsel, but that "the best thing the Senate could do is just bring this bill to the floor and vote on it."

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Calls for a vote on legislation to block Trump's ability to fire Mueller have grown in recent weeks after the president replaced Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE as attorney general with Whitaker, who has spoken critically of the special counsel's investigation.

McConnell on Wednesday blocked Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R-Ariz.) from bringing such legislation up for a Senate vote. In response, Flake said he'll oppose any of Trump's judicial nominations until McConnell brings a bill to protect Mueller to the floor.

The two men clashed on Thursday over the matter. A number of Republicans have said they support bringing the bill up for a vote, though some have expressed skepticism about its legality and its necessity.