WASHINGTON—House Republicans elected Rep. Kevin McCarthy of California as their new majority leader Thursday in a bid to restore stability to the fractious group of lawmakers buffeted both by internal divisions and the sudden defeat of their departing leader, Rep. Eric Cantor of Virginia.

Mr. McCarthy, currently the majority whip, will become the second-ranking House Republican at a time when party leaders are seeking to minimize policy splits leading up to November's midterm elections. Rep. Steve Scalise of Louisiana, who currently chairs the conservative Republican Study Committee, was elected to succeed him as whip, a job whose responsibilities include lining up votes and finding unity in the sometimes unruly Republican conference.

House Republicans have seen few periods of peace over a long string of leaders and the current group's uneasy alliance of business-friendly lawmakers and tea-party-backed conservatives has produced tensions reignited by Mr. Cantor's primary defeat last week.

The swift ascension of Mr. McCarthy, first elected to Congress eight years ago, is unlikely to alter GOP leaders' plans for a quiet legislative agenda this summer, but lawmakers hope his widespread popularity could knit together the often wayward group of Republicans.

Eager to present a united front to voters in the fall, Republicans have kicked the most contentious fiscal issues, including the next debt-ceiling increase, until after the midterms. Though House Speaker John Boehner (R., Ohio) has expressed support for considering an immigration overhaul, leaders aren't expected to bring up the bitterly divisive issue this summer.