U.S. Rep. Steve Scalise, of Jefferson, will run for the position of House majority whip as part of the Republican leadership scramble set off by the unexpected defeat of U.S. House Majority Leader Eric Cantor in a Virginia primary, Scalise said Wednesday.

The post of whip is No. 3 in the U.S. House majority pecking order, after House speaker and majority leader. The current whip is Kevin McCarthy, of California, who said he would run for majority leader.

Cantor plans to step aside from the leadership position July 31 in the aftermath of his defeat Tuesday night in a primary election to David Brat, a little-known and underfunded rival backed by tea party groups.

Cantor told fellow Republicans during an emotional, closed-door meeting Wednesday that he would serve out his House term. He then made a public announcement at a news conference where he appeared upbeat.

Republicans set leadership elections for June 19, assuring that any Capitol Hill campaigning will be brief.

Even before Cantor’s announcement, jockeying had broken out among fellow Republicans eager to move up the House leadership ladder — or establish a foothold on it.

The position of speaker is established in the U.S. Constitution, and the speaker is elected by the entire House, although the majority party effectively controls the selection. The other positions in the majority leadership are filled through voting by members of the majority party.

Scalise, 48, is chairman of the Republican Study Conference, an adamantly conservative coalition that includes most of the House’s Republican majority. That provides him with a solid base from which to challenge for the whip position — and given the vote in Virginia against Cantor, the right may demand a bigger slice of the leadership pie at the expense of more mainstream Republicans.

But Scalise, who has served in the House since 2008, won’t have a clear path to the whip job. Republican Rep. Pat Tiberi, of Ohio, identified Scalise and current Deputy Whip Peter Roskam, of Illinois, as the two declared candidates for the position, and other contenders may emerge.

One potential advantage for Scalise: He’s from a solidly red state that voted for the Republican ticket in the 2008 and 2012 presidential elections — unlike Virginia, California, Illinois or Ohio, the home state of Speaker John Boehner. Some conservatives have argued that red states deserve more representation in the top levels of the House hierarchy.

Even before Cantor’s defeat, Scalise was planning to run for whip in the event that a change of any kind in the leadership set off a game of musical chairs, Republican sources said. Boehner’s hold on the top job is not viselike, and the results of the November elections could strengthen existing challenges to him from within Republican ranks and create an opening, notwithstanding Cantor’s fate.

That potential timetable was affected and accelerated by Cantor’s rout in the primary in the Richmond suburbs he has represented since 2001.

Traditionally, the whip is responsible for enforcing party discipline and “whipping” party members to vote the party line. In the TV program “House of Cards,” the lead character of Frank Underwood begins the series as House majority whip.

If successful in his candidacy for whip, Scalise would become arguably the state’s highest-ranking Republican House member in history. Republican Bob Livingston, his 1st Congressional District predecessor, served as chairman of the House Appropriations Committee and was poised to become speaker in 1999 until revelation of an extramarital affair prompted him to drop out of the running.

In addition to McCarthy, U.S. Reps. Pete Sessions and Jeb Hensarling, both Texans, are eyeing a chance to succeed Canter.

House Speaker Boehner issued an appeal for cohesiveness at the closed-door meeting where he praised Cantor. “This is the time for unity, the time for focus,” he said in remarks released by his office.

The outcome of Tuesday’s primary represented the biggest victory by far this year for tea party forces, and it holds the potential to unsettle other incumbents facing GOP challengers this summer.

The next major showdown is a June 24 runoff between six-term U.S. Sen. Thad Cochran of Mississippi and his rival, state Sen. Chris McDaniel.

Cantor, 51, sounded like anything but a man ready to retire from politics, saying he would be active this fall for Republican candidates.

“What divides Republicans pales in comparison to what divides us as conservatives from the left and their Democratic” allies, Cantor said.

His pending resignation from his leadership post would mark a swift end to a quick rise to power for Cantor was appointed to the leadership two years after his election to Congress 14 years ago, and then rose steadily to become the second-most powerful Republican in the U.S. House. In that post, he was the most powerful Jewish Republican in Congress, and occasionally was seen as a potential rival to Boehner but more often as a likely successor.

Accused by tea party critics of being too accommodating on immigration and other issues, and criticized by Democrats for being inflexible, Cantor said he had struck the right balance. “I think that this town should be about trying to strike common ground,” he said.

But one Republican said he feared the effects of Cantor’s defeat could be debilitating for the party and the government.

Interviewed on MSNBC, Rep. Peter King, R-N.Y., said he was worried that Cantor’s stunning loss may lead to even more congressional gridlock. Asked if he thought immigration legislation was dead, he replied, “I’m concerned that Ted Cruz supporters, Rand Paul supporters, are going to use this as an excuse” to shut down the government.

“This is not conservatism to me,” King said. “Shutting down the government is not being conservative.”

David Espo, Andrew Taylor, Alan Fram and Erica Werner of The Associated Press contributed to this report.