WASHINGTON (Reuters) - Conservative U.S. Republican Representative Jim Jordan said Thursday he will run for speaker of the U.S. House of Representatives if his party keeps the majority after November elections, promising to slash federal spending and revamp the way the chamber is now run.

Jordan, one of the most influential conservatives in Congress, sent a letter to his colleagues announcing his decision. The current speaker, Republican Paul Ryan, is not running for re-election this fall.

“I plan to run for speaker of the House to bring real change to Congress,” Jordan declared in the letter. He pledged to pursue deep federal spending cuts, a repeal of the Affordable Care Act - former President Barack Obama’s landmark health insurance law - and a “complete shakeup” of the process for choosing committee heads.

Jordan is a co-founder and former chairman of the House Freedom Caucus group of hard line conservatives.

Recently several former wrestlers at Ohio State University accused Jordan, a former wrestling coach, of failing to stop molestation by an athletic doctor at the university years ago. Jordan has denied the allegations.

Ryan has thrown his support behind House Majority Leader Kevin McCarthy to replace him as speaker if Republicans control the chamber next year. McCarthy has been building strong ties with President Donald Trump, who could also influence the race for speaker.

Waiting in the wings if McCarthy falters is the No. 3 House Republican, Representative Steve Scalise, who was seriously injured in a shooting a year ago.

The House speaker is second in line for the presidency, behind the vice president, if the U.S. president dies in office or can no longer serve for other reasons. He also sets legislative priorities in the unwieldy 435-member chamber.

On Nov. 6, all 435 seats will be up for grabs.

Jordan, 54, has a long record of trying to make deep cuts in federal spending, except for the military. He has often clashed with Republican leadership over fiscal policy and last year was the target of Trump’s wrath over strategy for repealing the Obamacare healthcare law.

If Democrats win control of the House in November’s elections, Democratic Leader Nancy Pelosi is expected to make a bid for speaker. In 2007 she became the first female House speaker, serving in that job until 2011 when Republicans regained their majority.

Sometime after the election, Republicans and Democrats will gather separately to determine who their party leaders will be in the next Congress that convenes in January.

Once the members of that Congress are sworn in, the full House will vote on who will be speaker through 2020.