UPDATE 4:46 p.m.: At a news conference, Cantor said he "will be stepping down as majority leader" effective July 31. "It is with great humility that I do so," he said.
At the start of the news confence, Cantor cited his Jewish faith, saying, "While I suffered a personal setback last night, I couldn't be more optimistic about the future of the country." The presser came before a 4 p.m. meeting in which Cantor reportedly quoted a Holocaust survivor and said, "Suffering is a part of life. Misery is a choice," according to Politico reporter Jake Sherman.
The No. 2 Republican declined to explain his loss to challenger Dave Brat -- an upset that shocked the political establishment. He downplayed any friction between mainstream Republicans and the Tea Party.
"I'm going to leave the political analysis to y'all," he told reporters.
Asked who he would want to succeeed him as majority leader, Cantor didn't directly address the question, but said if his ally and House Majority Whip Kevin McCarthy of California throws his hat into the ring, "I think he'd make an outstanding majority leader and I'll be backing him with my full support."
Cantor said the election didn't dampen his outlook on America's future.
"While I may have suffered a personal setback last night, I couldn't be more optimistic about the future of this country," he said.
He also also ruled out a write-in campaign for his seat in the general election. Although he won't be on the ballot, Cantor said, "I will be a champion for conservatives across the nation."
UPDATE 3:06 p.m.: Cantor scheduled a 4:30 p.m. news conference to announce he'll give up his House majority leader post, according to Hill reporter Erik Wasson:
Cantor to hold 4:30 pm press conference to announce resignation
â€” Erik Wasson (@elwasson) June 11, 2014
House Majority Leader Eric Cantor, R-Va., isn’t waiting for his official ouster from Congress to step down from his leadership post.
According to Bloomberg, the No. 2 House Republican plans to step down as majority leader on July 31. The move is expected to be announced at a Republican caucus meeting starting at 4 Wednesday afternoon.
Cantor lost Tuesday’s Republican primary for his Virginia House seat to Tea Party-backed challenger and economics professor David Brat in an upset that shocked the political establishment.
A number of contenders have already started campaigning to replace Cantor as House majority leader, although a congressional source told Bloomberg that Cantor ally and House Majority Whip Kevin McCarthy, R-Calif., is considered to be the frontrunner.
Other Republicans who are expected to run to be House Speaker John Boehner’s deputy include Reps. Cathy McMorris Rodgers of Washington and Jeb Hensarling and Pete Sessions, both of Texas.
"Members are freaking out right now," a senior House GOP source told Fox News, referring to the flurry of calls lawmakers are receiving from candidates looking to succeed Cantor.