WASHINGTON — Representative Jim Jordan of Ohio, a powerful hard-line conservative who has been embroiled in a sexual abuse scandal from his days as a college wrestling coach, announced on Thursday that he will run to succeed Paul D. Ryan as House speaker.

Mr. Jordan’s bid is sure to roil the already shaky succession of power that Mr. Ryan set in motion when he announced that he would retire at the end of the year. Publicly, Republican leaders have backed the House majority leader, Kevin McCarthy of California. Privately, some Republicans have said Mr. McCarthy would not be able to unite the fractious party, and the No. 3 Republican in the House, Steve Scalise of Louisiana, is waiting in the wings.

Now comes the divisive figure of Mr. Jordan, who has the backing of the small but important House Freedom Caucus, which he founded, and outside conservative groups that have been pushing him to run. He has divided Republicans repeatedly with his aggressive tactics, most recently this week by filing articles of impeachment against the deputy attorney general, Rod J. Rosenstein.

Mr. Ryan responded Thursday by saying he would not back the action, and the House left for its monthlong August recess without taking it up.