JERUSALEM — While gliding to a surprisingly easy victory over Kadima party Chairwoman Tzipi Livni, Israel's newly elected opposition leader, Shaul Mofaz, faces an uphill battle in keeping the once-dominant centrist political party from splintering.

The Iranian-born Mofaz, 64, comfortably defeated Livni in Tuesday's primary, garnering nearly 62% of the vote in the party election. Speaking Wednesday, he wasted no time in setting his sights on Israel's next national election, which is not scheduled until the end of 2013 but which many believe may be called as early as this fall.

"I will lead Kadima to a victory over [Israeli Prime Minister Benjamin] Netanyahu," said Mofaz, a former defense minister who has been fighting for years to serve as chairman of Kadima and win a shot at the prime minister's job.

Mofaz is considered well-organized and politically savvy and has better relations with Israel's religious parties than does Livni. But it remains to be seen whether he can rescue Kadima, which three years ago won more votes than any other party but now is trailing badly in opinion polls.

Previewing his strategy, Mofaz on Wednesday emphasized social reform and easing Israel's high cost of living as top priorities, rather than focusing on reaching a peace deal with Palestinians, which was Livni's leading concern. But he will face the same challenges that Livni did in bringing together Kadima members, a diverse mix from Israel's left and right who followed then-Prime Minister Ariel Sharon in his break from the rightist Likud Party in 2005.

Some, including Livni during the recent campaign, said Mofaz, a former Likud member with strong security credentials, does not offer a clear enough alternative to Netanyahu, the Likud leader. Some say he might even opt to join Netanyahu's coalition government. Livni, by contrast, had steadfastly refused, arguing that Kadima's presence in the coalition would be used only as a "fig leaf" because Netanyahu had no intention of reaching a peace deal with Palestinians.

Some analysts say Mofaz's conservative credentials may eventually help him lure away votes from Likud.

"Since Mofaz is center-right, he has more of a capability than Livni to pull in disappointed Likud members and the soft-right-wing votes," said independent political analyst Raanan Gissin, who served as an advisor to Sharon. "That could change the balance."

In his speech, Mofaz called on Livni to remain in the party, but she refused to comment Wednesday about her plans. Supporters say she is considering dropping out of politics entirely, though others speculate that she might take time off or perhaps form a new party, potentially stealing away some of Kadima's members.

"Your place is with us," Mofaz said to Livni.

The election results are a stinging rebuke to Livni, a former foreign minister once on track to become Israel's second female prime minister. Despite her sagging domestic popularity, Livni was one of Israel's most popular politicians internationally, thanks to her oft-stated commitment to helping create a Palestinian state that would end the long-standing Middle East conflict.

"Such a vote of no-confidence by registered voters in the leader of their party is something that we have not seen in a long time, if ever," wrote newspaper columnist Sima Kadmon in Wednesday's Yediot Aharonot. "Ouster, that is the word."

The fallout will become clearer in the coming weeks, but there's no question that Tuesday's election marked a turning point for Kadima, a party that holds more Knesset seats than any other but nevertheless has been made largely irrelevant by the Likud-led right-wing coalition.

Yet a split in the party may not be as bad as some fear since it might reduce infighting that has gone on since 2008 and enable leaders to formulate a clearer platform on issues.

When Defense Minister Ehud Barak broke away from the leftist Labor Party last year and formed a new party, the fracture served to only revitalize Labor. At the time, many pundits wrote off Labor as dead, but it is now performing better than Kadima in most polls.