A bipartisan group of senators unveiled a compromise bill Wednesday to give Special Counsel Robert S. Mueller III job protections, as renewed criticism from President Donald Trump adds more fuel to speculation that he plans to fire the man tapped to investigate connections between his campaign and Russian operatives.

Trump on Wednesday dubbed Mueller’s probe the “Fake Corrupt Russia Investigation” on Twitter, the latest in a series of statements sparked by the FBI’s search Monday of the office of his personal lawyer Michael Cohen. It is one of several times since June that Trump’s statements have prompted discussion that Mueller’s job was at risk.

Senate Judiciary Committee Chairman Charles E. Grassley, on a conference call with Midwest reporters, said the new bill would probably be on the committee’s agenda Thursday but might not get a vote until next week.

Still, there was no immediate sign that Majority Leader Mitch McConnell, R-Ky., planned to bring such legislation to the floor, or that such a bill could pass in the Republican-controlled House.

The new bill would turn into law the current Justice Department regulations that ensure a special counsel can only be fired for cause by a senior department official who puts the reasons in writing. Passing such legislation would address some concerns that Trump could repeal the regulations as one path to remove Mueller.

The proposal also would give a special counsel 10 days to ask a federal judge to review whether a removal was for good cause, and if not, allow the special counsel to stay in the job. It would also require staffing, documents and materials of the investigation to be preserved.

The measure combined two bills, first introduced eight months ago amid one of the first instances Trump’s words caused concern that he would fire Mueller. The senators behind those bills, Republicans Lindsey Graham of South Carolina and Thom Tillis of North Carolina and Democrats Chris Coons of Delaware and Cory Booker of New Jersey, combined their efforts for the measure released Wednesday.

“This is a time when all of us — Republicans and Democrats — need to stand up and make it clear that we are committed to the rule of law in this country,” Coons said in a news release. “We need to ensure not only that Special Counsel Mueller can complete his work without interference, but that special counsels in future investigations can, too.”

McConnell and other Senate Republicans told reporters Tuesday that such a law isn’t needed and that they don’t think Trump will fire Mueller.

“I haven’t seen a clear indication yet that we needed to pass something to keep him from being removed because I don’t think that’s going to happen, and that remains my view,” McConnell said.

White House Press Secretary Sarah Huckabee Sanders, when asked Tuesday if Trump has the authority to fire Mueller, said that “we’ve been advised that the president certainly has the power to make that decision.”

Democratic lawmakers have warned that Trump could spark a constitutional crisis or risk impeachment if he fires Mueller, or Deputy Attorney General Rod Rosenstein. Trump has called out Rosenstein by name because he oversees the Mueller probe and legal experts say he is the official who can fire Mueller under current DOJ regulations.

“Why not pass this legislation now and avoid a constitutional crisis?” Minority Leader Charles E. Schumer, D-N.Y., said on the floor Wednesday. “Why not avoid an injury to the body of this great country and then try to stitch it up? That’s what we should be doing. Let’s not wait until it’s too late.”

Rosenstein has told Congress that Mueller, a former FBI director appointed by Republican President George W. Bush, has acted appropriately and within the bounds of his role as special counsel. 

Trump repeatedly has called the Mueller probe a “witch hunt.” The New York Times reported in January that Trump ordered the firing of Mueller and backed down when White House Counsel Donald McGahn threatened to resign. Trump criticized the Mueller probe in March after Attorney General Jeff Sessions fired former FBI Deputy Director Andrew McCabe, and again Wednesday.

Despite the probe being led by lifelong Republicans, Trump tweeted Wednesday that it is being “headed up by the all Democrat loyalists, or people that worked for Obama.”

The president called Mueller the “most conflicted of all (except Rosenstein who signed FISA & Comey letter). No Collusion, so they go crazy!”

John T. Bennett contributed to this report.