Republicans on the Senate Judiciary Committee are pushing for a bill to protect special counsel Robert Mueller, despite a vow from Senate Majority Leader Mitch McConnell that it won’t reach the floor for a full vote.

Committee Chairman Chuck Grassley decided Thursday to delay markup on the legislation — the Special Counsel Independence and Integrity Act — until next week.

And he defended the legislation despite McConnell's pledge to kill it.

Grassley said he gave his word to the sponsors of the legislation that “if you can get together to have a bill, we’ll have a bill. Then that’s why it’s on the agenda."

“Just in case anybody in the leadership of the Republican Party of the United States Senate or even on this committee, they’ll know why, as chairman of this committee, I’m moving forward,” the Iowa Republican said.

In a Fox News interview Tuesday, McConnell said he wouldn’t put the bill on the floor because he didn’t think President Trump would fire Mueller.

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

The bill is bipartisan, 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.

On Thursday, Graham said he doesn’t think Trump will fire Mueller, but the legislation is still important.

“But I’m looking at the special counsel from an institutional point of view. Is the special counsel a political appointee? Are they a civil servant? There is actually due process. What I’m trying to do is look at the special counsel as someone who’s a hybrid — and they need some protection, and they need some due process,” Graham told reporters Thursday. “It’s very much constitutional I think to have a check and balance over a special counsel who is a hybrid status.”

The legislation, introduced earlier this month, ensures Mueller can only be fired for “good cause” by a senior Justice Department official. It also states that if he were fired, Mueller has a 10-day time period to seek an expedite judicial review of his firing to review if it were for good cause.

“We’ve had a lot of history with independent counsels … and the challenge is to provide some accountability. Constitutionally [Trump] has that power, but i think it would be a mistake to do that. He needs to complete his investigation and we need to keep doing our work,” Sen. John Cornyn, R-Texas, said Thursday.

“At the very least, if it's passed out of this committee, it's ready and it could go at any time on the floor," Sen. Dianne Feinstein, the ranking Democrat on the committee, said Thursday.