While Republicans have a slim majority, Kevin McCarthy, the party's leader in the House, has been unable to sway a small but staunch faction of far-right representatives so far unwilling to elevate him to the job.
He fell short on a sixth ballot Wednesday.
Voting will resume Thursday without any sign of an end to the gridlock.
The Speaker contest marks the first time in a century that the election has gone beyond a first round of voting.
The Republican infighting comes despite a plea from former president Donald Trump to unite behind McCarthy.
The Democratic leader, Hakeem Jeffries, has so far come out with the most overall votes in six straight ballots, but not a majority.
