A majority of G.O.P. lawmakers had yet to declare a preference between the two announced candidates, and former Speaker Kevin McCarthy was leaving the door open to a return to the post.
Less than a week after his ouster, the former speaker indicated he would be open to reinstatement as Republicans prepared to discuss whom to nominate to succeed him.
The second-ranking Republican, who was cut out of major decisions by the previous speaker, is pitching himself as uniquely positioned to unify the deeply divided House G.O.P.
A quiet fight over the rules highlights the depth of G.O.P. divisions. It could set the stage for a bruising election to choose a successor to the party’s ousted speaker.