Republicans started walking out of the House chamber during the fourth day of a battle over electing Kevin McCarthy as their speaker when one of his most ardent challengers railed against the party leader.

“We do not trust Mr McCarthy with power,” said Republican Matt Gaetz of Florida, as colleagues streamed out of the chamber in protest over his remarks.

However, there were signs of softening of the holdouts’ opposition to Mr McCarthy. At least five of them flipped to vote for him as balloting resumed.

The 12th vote in a stand-off that is testing American democracy, took place against the backdrop of the anniversary of the January 6 attack on the Capitol, which shook the country when a mob of then-president Donald Trump’s supporters tried to stop Congress from certifying the Republican’s 2020 election defeat to Democrat Joe Biden.

As talk of a deal with conservative holdouts who have been blocking Mr McCarthy’s rise emerged, it was still out of reach after three dismal days and 11 failed votes in a political spectacle unseen in a century.

Arriving at the Capitol on Friday morning, an upbeat Mr McCarthy said to reporters: “We’re going to make progress. We’re going to shock you.”

Voting resumed after Republican Mike Garcia nominated Mr McCarthy for a 12th time, also thanking the US Capitol Police who were given a standing ovation for protecting lawmakers and the legislative seat of democracy on January 6.

The chamber is unable swear in members and begin its 2023-24 session. Mr McCarthy told lawmakers there were no plans to adjourn for the weekend, one Republican said, but it might be difficult to keep them in Washington DC.

So far Republicans have been unable to settle on a new speaker — normally an easy, joyous task for a party that has just won majority control. But not this time: About 200 Republicans are hampered by 20 far-right colleagues who say he is not conservative enough.

The agreement Mr McCarthy presented to the holdouts from the conservative Freedom Caucus and others centres around rules changes they have been seeking for months.

Those changes would shrink the power of the speaker’s office and give rank-and-file lawmakers more influence in drafting and passing legislation.

Even if Mr McCarthy is able to secure the votes he needs, he will emerge as a weakened speaker, having given away some powers, leaving him constantly under threat of being voted out by his detractors.

But he would also be potentially emboldened as a survivor of one of the more brutal fights for the gavel in US history.