(NewsNation) — Republican leaders floated the idea of changing the requirements for removing a House speaker from power, but current House Speaker Mike Johnson, R-La., says he has no plans to do so.

A source previously told NewsNation some GOP representatives had wanted to make it so that it takes more than one person to start the process of ousting a speaker.

Johnson said on X Thursday afternoon that “many members” have encouraged him to endorse that new rule.

However, he said such a change would require a majority of the full House of Representatives, which the Republicans do not have.

“We will continue to govern under the existing rules,” Johnson said. Still, he criticized the single-member motion to vacate as something that has “harmed this office.”

The discussions come as Johnson’s position is under threat by Reps. Marjorie Taylor Greene, R-Ga. and Thomas Massie, R-Ky. Both want Johnson to back down on funding for Ukraine. A motion to vacate resolution, as it’s known, was filed by Greene last month, the Associated Press reported, and Massie told colleagues he will co-sponsor the effort.

Neither lawmaker has said when a vote on Johnson’s removal could come to the floor.

Johnson on Tuesday criticized the efforts to oust him as “absurd.”

“It is not helpful to the cause, it is not helpful to the country, it does not help the House Republicans advance our agenda which is in the best interest of the American people here — a secure border, sound governance — and it’s not helpful to the unity that we have in the body,” Johnson said at a news conference where he stressed he is not resigning.

While voting Johnson out as speaker would be a rare move by historical standards, this would be the second time in the past year that it’s happened. His predecessor, former Rep. Kevin McCarthy, R-Calif., was voted out of the speakership last year in an effort orchestrated by Republican Rep. Matt Gaetz of Florida. It had been McCarthy who cut a deal with conservatives allowing for a single member to bring a resolution to remove the speaker when he was first vying for the position, NewsNation partner The Hill noted.

On Thursday, Johnson held firm on his decision to support a foreign aid package that would include about $61 billion for Ukraine. Some conservatives, though, have been opposed to sending more financial assistance to Ukraine, arguing that the United States should be focusing on its own problems — particularly security at the U.S.-Mexico border.

Johnson, however, has said the threat of Russian President Vladimir Putin winning the war against Ukraine and taking on other NATO allies next is a risk that can’t be taken.

“This is not a game, it’s not a joke. We can’t play politics with this. We have to do the right thing and I’m going to allow an opportunity for every single member of the House to vote their conscience and their will on this,” he said.

The Hill reported that Johnson said he plans to move a separate border bill as the House considers foreign aid measures.

Greene called this “theatrics.”

“It’s the shiny object for Republicans that are saying we got to do something for the border,” she said.

While the House is expected to vote on this border bill in the coming days, it will likely still face a dead end in the Senate, as many of its provisions are nonstarters among Democrats.

NewsNation reporter Evan Lambert, digital producer Devan Markham and The Associated Press contributed to this report.