(CNN) Senate Judiciary Committee Republicans are plowing ahead with their plan to pass a bill out of the committee that would protect special counsel Robert Mueller, despite Majority Leader Mitch McConnell's vow not to put the measure on the Senate floor.

Senate Judiciary Chairman Chuck Grassley, an Iowa Republican, put the bill on his committee's agenda for a markup Thursday, which under the panel's rules means it will it will come before the committee next week.

Grassley said that he was unconcerned about McConnell's vow that he wouldn't bring the bill to the floor, saying it was irrelevant to his committee's work.

"Obviously the views of the majority leader are important to consider, but they do not govern what happens here in the Judiciary Committee," Grassley said. "If consideration on the floor was the standard for approving a bill in committee or not, we wouldn't probably be moving any bills out of this committee."

The bill, which was co-authored by Republican Sens. Thom Tillis of North Carolina and Lindsey Graham of South Carolina and Democratic Sens. Chris Coons of Delaware and Cory Booker of New Jersey, would make it harder for President Donald Trump to fire Mueller by allowing Mueller to seek a 10-day expedited judicial review if he's dismissed.

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