The US House speaker, Mike Johnson, asked fractious fellow Republicans to “cool it” and stop fighting each other in displays of “member-on-member action” during primary elections as he seeks to maintain some sort of control over a caucus at the mercy of the far right, controlling the chamber by a mere two votes.

“I’ve asked them all to cool it,” Johnson told CNN in remarks published on Sunday. “I am vehemently opposed to member-on-member action in primaries because it’s not productive. And it causes division for obvious reasons, and we should not be engaging in that.

“So I’m telling everyone who’s doing that to knock it off. And both sides, they’ll say, ‘Well, we didn’t start it, they started it.’”

The Florida congressman Matt Gaetz, the far-right Trumpist firebrand pursuing such fights, in effect told the same outlet: “They started it.”

“I would love nothing more than to just go after Democrats,” said Gaetz, who was last year the prime mover behind the historic ejection of Johnson’s predecessor as speaker, Kevin McCarthy, and who is now going after two more Republicans, Tony Gonzales of Texas and Mike Bost of Illinois.

“If Republicans are going to dress up like Democrats in drag, I’m going to go after them too,” Gaetz said. “Because at the end of the day, we’re not judged by how many Republicans we have in Congress. We’re judged on whether or not we save the country.”

Gonzales is under attack over a vote for gun safety reform, after the Uvalde elementary school massacre; over his positions on immigration reform; and for voting in favour of same-sex marriage.

“What happened in Uvalde should have never happened,” Gonzales told CNN. “Not because [the gunman, who killed 19 children and two teachers] was 18 years old. Not because it was an AR[-15 rifle], because he was batshit crazy, right? So crazy people should not have access to kill innocent people.”

On same-sex marriage, Gonzales added: “Look – I’m a father of six. Whatever a gay is, I’m about as further away as far away from that as possible. But I’ve served with all different kinds of people in the military … I look at … the merit of an individual.”

Asked about Gaetz campaigning against him, Gonzales said: “Who?”

Asked about the primary opponent Gaetz is supporting, Brandon Herrera, a gun salesman and YouTube personality, Gonzales said: “I don’t even know what a YouTuber does.

“I mean, I know what I did to become a [navy] master chief: I busted my ass, I fought in two wars.”

Master chief petty officer is the highest enlisted rank in the US navy. Gonzales was a cryptologist.

He told CNN he was “not worried” about Gaetz but also indicated, in words perhaps disappointing to Johnson, that he was happy to fight.

“Anyone who wants to come against me, pop their heads out,” he said.