By Peter Schroeder and Rebecca Shabad - 06/11/14 01:22 PM EDT
Rep. Darrell Issa (R-Calif.) confirmed the news to reporters at the Capitol.
House Majority Whip Kevin McCarthy (R-Calif.), the No. 3 House Republican, is planning to run for Cantor’s second-ranking post, and Issa said he expected to Cantor to back him.
Rep. Pete Sessions (R-Texas) is planning to challenge McCarthy. Sessions, the chairman of the House Rules Committee and a former GOP campaign chief, began making calls to colleagues after Cantor’s loss, seeking support.
Reps. Steve Scalise (R-La.) and Peter Roskam (R-Ill.) are expected to pursue McCarthy's postion.
And Rep. Jeb Hensarling (R-Texas), a favorite of conservatives, said Wednesday's he's been approached about running for leadership. Some see Hensarling as a possible contender for the House speakership.
Rep. Mick Mulvaney (R-S.C.), a vocal conservative gunning to be chairman of the Republican Study Committee, told reporters he will support Hensarling for majority leader but did not know if he would run.
Cantor lost his primary to Tea Party-backed Dave Brat 56 percent to 44 percent.
First elected to Congress in 2000, Cantor decided not to run as a write-in candidate to try to save his seat.
The Washington Post first reported the news that Cantor would step down.
This story was updated at 1:42 p.m.