Another bipartisan group of senators is trying to make it harder for President Trump to fire the special counsel investigating him and his presidential campaign.

Sens. Lindsey Graham, R-S.C., Cory Booker, D-N.J., Sheldon Whitehouse, D-R.I., and Richard Blumenthal, D-Conn., introduced a bill Thursday afternoon aimed at preventing the firing of special counsel Robert Mueller.

A bill introduced by Sens. Thom Tillis, R-N.C., and Chris Coons, D-Del., earlier on Thursday would allow the special counsel to challenge his or her firing in court.

Graham had promised last week that such legislation would be coming. In his bill, a Justice Department official planning to fire the special counsel — in this case Deputy Attorney General Rod Rosenstein — would have to go before a panel of three federal judges to get approval.

"Any effort to go after Mueller could be the beginning of the end of the Trump presidency unless Mueller did something wrong," Graham told reporters last week.

Rosenstein appointed Mueller to lead a probe into Russia's meddling in the 2016 presidential election after Attorney General Jeff Sessions recused himself.

Rosenstein told a Senate Appropriations subcommittee in June he would remove Mueller "only for good cause."

"And I am required to put that cause in writing. That's what I would do. If there were good cause, I would consider it," Rosenstein told the senators. "If there were not good cause, it wouldn't matter to me what anybody says."

Though Trump has not said publicly that he plans to fire Mueller — who he has openly criticized for various reasons — reports say he has considered doing so.

However, former White House spokesman Sean Spicer told reporters in late June that while Trump "retains the authority" to dismiss Mueller, "he has no intention of doing that."