Washington(CNN) Senate Majority Leader Mitch McConnell told Fox News on Tuesday he doesn't believe President Donald Trump will fire Robert Mueller, adding he doesn't want legislation on the issue.

"I don't think he should fire Mueller and I don't think he's going to," he said in the interview. "So this is a piece of legislation that isn't necessary in my judgment."

Last week, a bipartisan group of senators introduced legislation that would make it harder for Mueller to be fired for investigating Russian meddling in the 2016 election.

Sens. Lindsey Graham, a South Carolina Republican, Chris Coons, a Delaware Democrat, Thom Tillis, a North Carolina Republican, and Cory Booker, a New Jersey Democrat, introduced the Special Counsel Independence and Integrity Act, which protects Mueller, including ensure that the special counsel can only be fired for "good cause" by a senior Justice Department official.

McConnell said he won't bring the legislation to the Senate floor.

"I'm the one who decides what we take to the floor, that's my responsibility as the majority leader, we will not be having this on the floor of the Senate," he said.

When asked if he'll be shocked if Trump fired Mueller, McConnell responded, "Yes, I don't think he should and I don't think he will."

Coons told CNN he still wants a committee markup, despite what McConnell said.

"I don't know from where Leader McConnell gets his confidence Trump will not take action to interfere with this investigation," he said. "Given the number of times in recent days the President has tweeted or spoken directly or indirectly in ways that I think threaten the investigation led by Special Counsel Mueller."

He continued: "I'm focused on making sure we get to a mark-up on the Judiciary Committee next Thursday and that we're in a place for it to get passed the Judiciary Committee."

Senate Minority Leader Chuck Schumer responded to McConnell's interview in a statement, saying it's a mistake not to pass the legislation.

"While I'm glad the majority leader believes the President would be wrong to fire Special Counsel Mueller, it's a mistake not to pass legislation to protect the investigation," he said in a statement. "We ought to head off a constitutional crisis at the pass, rather than waiting until it's too late. ... I hope the Judiciary Committee moves forward with a bill, and that members of Senator McConnell's caucus push him to reconsider."

Sen. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, said it was still important for the committee to pass legislation protecting the special counsel even if McConnell wouldn't put it on the floor.

She suggested it would send message, and also be available if circumstances surrounding Mueller ever changed.

"If a bill came out of the Judiciary Committee with the votes, and I don't know that it would, but it seems to me that bill is there," Feinstein said. "And depending on circumstances regardless of if he would put it on at a certain time, it would be there. And that accomplishes something."

This story has been updated to include additional lawmakers' reactions.