The American House of Representatives did not elect a speaker in the twelfth ballot on Friday.
Republican faction leader Kevin McCarthy came much closer to his goal of becoming the third highest office in the United States.
He received 213 votes, 13 more than in Thursday's last three ballots.
Only seven of the 20 Republicans who had supported other candidates in 11 rounds of voting again withheld McCarthy's vote.
In doing so, the majority of the rebels gave the lie to Florida MP Matt Gaetz, who had assured at the beginning of the session that the group of twenty MPs would remain closed.
Gaetz's speech, which nominated McCarthy's supporter Jim Jordan, contained the most severe criticism of McCarthy yet.
No power should be entrusted to him, because he will not use it in the interests of the people, but of the lobbyists.
It was the first time there had been movement in McCarthy's direction since Tuesday's first vote.
Democrat Hakeem Jeffries received 211 votes;
a member of his group was apparently absent.
From McCarthy's camp it was said that there would be another vote on Friday.
McCarthy had already announced on Friday morning that the public would be "shocked" at the meeting.
One of his concessions was that in future every single member of parliament can initiate a vote of no confidence against the "speaker".
In addition, the former dissenters should be allowed to determine two of nine members in the influential Rules Committee.
Every bill goes through the hands of the MPs on this committee.
McCarthy also agreed to hold a vote on MP term limits and specific border policy legislation.