Jordan, who has lost two votes for speaker this week, emerged from an hours-long closed-door meeting with fellow Republicans to say he would press ahead with a third vote.
It was not clear when the House would vote again on a speaker.
House Democrats and the White House have said they are open to that idea, but many Republicans rejected it.
He told fellow Republicans on Thursday that he would drop out of the speaker's race if his opponents were unmoved after talking with him, two lawmakers said.
One of those, Representative Drew Ferguson, said in a statement on Thursday: "The House Republican Conference does not need a bully as the speaker."
Persons:
Jim Jordan, Jordan, House Pro Tempore Patrick McHenry, Kevin McCarthy, Patrick McHenry, we're, Blaine Luetkemeyer, Joe Biden, Republican Steve Scalise, Drew Ferguson, McCarthy, shutdowns, Biden's, Biden, David Morgan, Makini Brice, Moira Warburton, Katharine Jackson, Nandita Bose, Davide Barbusca, Julio, Cesar Chavez, Andy Sullivan, Scott Malone, Nick Zieminski, Grant McCool
Organizations:
U.S . House, House Pro Tempore, Republicans, House Democrats, Democratic, AS, Republican, House Republican Conference, White, Democrats, Thomson
Locations:
WASHINGTON, Ukraine, Israel, Washington