Chaffetz, the chairman of the House Oversight Committee, on Sunday officially announced his underdog bid to challenge McCarthy.
He argues McCarthy is short of the 218 votes needed on the House floor to be elected Speaker. Democrats in that election are expected to back Minority Leader Nancy Pelosi (Calif.), meaning Republicans will need to unify behind their pick for the position.
Chaffetz has criticized a gaffe McCarthy made last week when he linked the Benghazi panel to Hillary Clinton’s falling poll numbers as a House Republican accomplishment.
The comments were widely criticized by Republicans as they suggested the panel investigating the 2012 terrorist attack on a U.S. facility in Benghazi, Libya was launched for political reasons.
Chaffetz has said the comments were “inappropriate” and called on McCarthy to apologize.
He doubled down on Monday while noting that McCarthy had walked back his comments.
“It was a terrible mistake, but it was a mistake,” Chaffetz said Monday of McCarthy’s remarks. “We have to move on.
“I think we need to take a fresh start. I think we need to take the fight to the American people. We need a Speaker who speaks and actually articulates our message,” Chaffetz said on MSNBC.
He noted upcoming legislative fights on issues such as raising the debt ceiling, ObamaCare and support for the military.
“We need to unite our conference and figure out where we’re going to hold the line,” Chaffetz said, emphasizing the need to send bills to President Obama’s desk.
Closed-door elections for Speaker and other GOP leadership spots are expected on Thursday.
The elections were triggered by Speaker John Boehner’s (R-Ohio) decision to resign last month. Boehner is serving as Speaker until the end of October.