JERUSALEM — After Israel's parliamentary election, which produced rival claims of victory by two candidates for prime minister, the difficult task of appointing one of them to form the next government falls to President Shimon Peres.

A seasoned politician now in an official non-partisan role, Peres will have to weigh the recommendations of political factions and do the hard mathematics of coalition-building in assigning the task to the candidate most likely to win the backing of a parliamentary majority.

Foreign Minister Tzipi Livni, who heads the centrist Kadima party, and Benjamin Netanyahu, leader of the rightist Likud party, began contacts Wednesday with other factions to sound out coalition prospects.

Kadima emerged as the largest faction in parliament, winning 28 seats, but Likud and other rightist factions control 65 seats in the 120-member legislature, making it easier for Netanyahu to form a governing coalition.

A Netanyahu-led coalition with other hawkish parties would have little interest in Middle East peace talks promoted by the new administration of U.S. President Barack Obama. And even if Livni manages to cobble together a coalition after weeks of political bargaining, she could be hindered by right-wing partners from pursuing her stated goal of negotiating a two-state solution to the conflict with the Palestinians.

Netanyahu and Livni met separately Wednesday with Avigdor Lieberman, whose ultra-nationalist Yisrael Beitenu party won 15 seats, becoming the third-largest faction in parliament. His backing is crucial for both candidates as they work to line up support by a majority in parliament.

Netanyahu also met with the ultra-Orthodox Shas faction, which controls 11 seats and said it would support his leadership of a new coalition.

Next week, Peres will meet with all parliamentary factions to hear their recommendations on who should form the next government. He is expected to assign the task to the candidate with the best chance of forming a majority coalition.

A longtime leader of the Labor party, Peres joined Kadima in his last year in politics. But analysts said it is unlikely he would use his official position to favor Livni, for whom the odds of forming a majority government appear slim.

"He won't try something that doesn't have a chance if the factions tell him Netanyahu has the support of the majority of parliament members," said Shmuel Sandler, a professor of political science at Bar-Ilan University. "He wouldn't want to appear as someone motivated by political considerations and not the people's will."

Abraham Diskin, a political scientist at the Hebrew University of Jerusalem, said that although the leader of the largest faction in parliament usually gets first crack at forming a coalition, there have been cases in which others were given that opportunity when it appeared they were more likely to succeed.

"Today it is quite clear that Peres is going to appoint Netanyahu, because realistically Livni doesn't have any chance of forming a coalition," Diskin said. "My guess is that Peres will try to persuade both Netanyahu and Livni to join forces and form a national unity government" under Netanyahu's leadership.

One idea being floated is that Netanyahu and Livni would alternate as prime ministers, each for two years of the government's term, but Netanyahu rejected that notion Wednesday.

A spokeswoman for Peres said he probably would assign the task of forming a coalition around Feb. 20.

Despite the uphill battle she faces to form a coalition, Livni sounded a note of determination Wednesday.

"The people chose me in droves," she told reporters. "I feel a great responsibility."

Netanyahu has said he wants to form a broad government to deal with the security and economic challenges facing Israel.

Analysts said he wants to avoid a narrow rightist government that could lead to diplomatic difficulties and put him on a collision course with Washington.

jogreenberg@tribune.com