Rep. Tom Cole (R-Okla.) suggested Wednesday that the House Ethics Committee should consider whether Rep. Marjorie Taylor Greene (R-Ga.) should lose her committee assignments rather than the full House.

Cole, who has served in the House for nearly two decades and is the top Republican on the Rules Committee, argued during a hearing on a resolution to remove Greene from the Education and Labor and Budget committees that it's a slippery slope if the majority party moves unilaterally to remove a member of the minority party from committees.

"The Ethics Committee should review the matter in question, determine if a new standard relating to actions taken by a member of Congress before they are elected should be covered by the code of conduct, and make the appropriate recommendations. Doing anything different would risk sending the institution down a precarious path, the end of which we cannot predict," Cole said.

Greene has come under fierce criticism not only from Democrats but from Senate Republicans over remarks backing the QAnon conspiracy theory, suggesting school shootings were faked and endorsing violence against Democratic office holders. 

Senate Republicans have made it clear she should not be a face of the party, with various members describing her as "loony," "not what the Republican Party stands for" and a "kook." The House will vote Thursday to remove her from committees. 

But House Republicans have been divided over Greene, who is supported by former President Trump. 

Cole suggested that the House Ethics Committee review if there should be a "new standard" to determine if lawmakers' actions before being elected should be subject to the chamber's code of conduct.

He stressed that he thinks Greene's incendiary comments were "deeply offensive," "repugnant" and "unbecoming of any member of Congress."

"I don't want you to take my statement as suggesting that I don't think action is appropriate. I just think the appropriate action is for the Ethics [Committee] to look at this and that's how we should proceed," Cole said.

But moments later, Rep. Jackie Walorski (Ind.), the top Republican on the House Ethics Committee, said that Greene's statements wouldn't fall under the panel's jurisdiction.

"The Committee on Ethics does not exercise its jurisdiction over statements made by a member of Congress that were not otherwise unlawful before they were sworn into office," Walorski said.

"The timing of the statements does not make them right, but the timing of the statements does put them outside the Ethics Committee's jurisdiction," Walorski added.

House Ethics Committee Chairman Ted Deutch (D-Fla.) — who represents Parkland, the site of a school shooting that Greene has spun conspiracy theories around — questioned the GOP argument that the Ethics Committee should review the Greene matter first.

"It's hard to argue that the committee doesn't have jurisdiction, but this should nevertheless go before the committee," Deutch said.

House Rules Committee Chairman Jim McGovern (D-Mass.) pointed to precedents of members of Congress losing their committee assignments following controversial conduct, like former Reps. William Jefferson (D-La.), who went to prison for bribery charges, and Steve King (R-Iowa), who made comments appearing to defend white supremacy after years of making inflammatory statements. In both cases, their parties' leadership removed them from committees.

House Minority Leader Kevin McCarthy (R-Calif.) met with Greene on Tuesday night, but she has been unrepentant and has been fundraising off the prospect of being removed from committees. The GOP Steering Committee, which determines committee assignments, also met Tuesday night but did not reach a resolution on Greene.

McGovern shrugged off the notion that booting Greene from committees would set a bad precedent.

"You know, if the precedent's going to be that if somebody advocates putting a bullet in the head of a member of Congress, and if that is going to be the new determination as to what it takes to throw people off of committees, I'm fine with that. I'm fine with that," McGovern said.