"If we are going to unite and be strong, we need a new face to help do that," McCarthy told reporters after informing House members of his decision.
McCarthy said he will retain his position as majority leader.
The decision came as House Republicans had gathered to vote on the next speaker, members told ABC News.
Two other House Republicans are running for House Speaker - Rep. Jason Chaffetz, R-Utah, and Daniel Webster, R-Florida. On Wednesday, Webster earned an important endorsement from the House Freedom Caucus, a key conservative group in the House of Representatives.
Earlier today, Chaffetz said he still considered himself an underdog, but said he didn't believe McCarthy would receive the magic 218 votes he needed to win the wider vote on the House floor on October 29th.
“Clearly, I’m an underdog. I get that. I ran because I’m trying to bridge the gulf and divide in the Republican conference and say hey, it’s time for a fresh start,” he told reporters.
Boehner, who last month announced he would step down from the speakership on October 30th, postponed the election.
“After Leader McCarthy’s announcement, members of the House Republican Conference will not vote today for a new Speaker. As I have said previously, I will serve as Speaker until the House votes to elect a new Speaker. We will announce the date for this election at a later date, and I’m confident we will elect a new Speaker in the coming weeks," Boehner said in a statement. "Our conference will work together to ensure we have the strongest team possible as we continue to focus on the American people’s priorities.”
"Kevin McCarthy is best person to lead the House, and so I’m disappointed in this decision. Now it is important that we, as a Conference, take time to deliberate and seek new candidates for the speakership," Ryan said. "While I am grateful for the encouragement I’ve received, I will not be a candidate. I continue to believe I can best serve the country and this conference as Chairman of the Ways and Means Committee.”
White House Press Secretary Josh Earnest said Republicans must select a speaker who is able "simply to unite a divided Republican caucus."
“There is a minority group of conservative politicians that places their own extreme ideology ahead of everything else and certainly ahead of effective governance of the country, but also as of today ahead of the effective governance of the House Republican caucus.” Earnest said “Somebody within the - among the house republicans will have to step forward and demonstrate an ability to either tame the forces of that, again small but vocal group of extreme ideologues, or buck up the mainstream or at least more mainstream majority within the House Republican conference that will also include a willingness to work in bipartisan fashion."
When he was asked whether there is a Republican the White House would like to see in the speakership, Earnest said, “My guess is an endorsement from me from here would well not be viewed as an endorsement."