Prime Minister Benjamin Netanyahu and his rival Benny Gantz held talks on Monday over a proposed Israeli unity government, and a key politician said the focus was on who would lead it first under a rotation deal.

Such a rotation has a precedent in the 1984-88 unity government of left-leaning Shimon Peres and right-winger Yitzhak Shamir, who took turns as prime minister.

Under Israeli law, the president should have appointed as prime minister the candidate he believes has the best chance of forming the next government after last week's do-over elections. But the voting yielded inconclusive results, leading Rivlin to call for a unity government.

President Reuven Rivlin, tasked with picking a candidate best-placed to try to form the next governing coalition, has spoken in favor of unity, and on Monday summoned Netanyahu and Gantz for closed-door talks.

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Local media aired the beginning of the trilateral meeting at the President's House in Jerusalem, attended by Rivlin, Netanyahu, and his main challenger Gantz.

"There is one thing the people are largely untied over and that is the desire that there won't be third elections," Rivlin said in a statement earlier on Monday.

Concluding their meeting at Rivlin's Jerusalem office, Netanyahu and Gantz issued a joint statement saying they had discussed "moving forward with unity," but did not elaborate.

Gantz, head of the centrist Blue and White Party, has openly rejected the idea of forming a coalition with Netanyahu's right-wing Likud, citing looming corruption charges against the incumbent.

He met earlier with Avigdor Lieberman, a political free agent and likely kingmaker thanks to his eight seats in parliament.

"Happily, the two big parties have internalized the pressing necessity of setting up a unity government with a rotating premiership," Lieberman said on Facebook while pointing out that "the entire argument right now is over the question of who will serve first as prime minister, and who second.

If a power-sharing deal is forged, it could be imperative for Netanyahu to serve as prime minister first should he seek to avoid prosecution.

Next month, Israel's attorney-general will hold a pre-trial hearing on his intention to indict the Israeli leader on fraud and bribery charges in three corruption cases. Netanyahu has denied any wrongdoing.

As prime minister, Netanyahu would be under no legal obligation to resign if formal charges are filed. But other cabinets post might not offer him that same protection.

The candidates' negotiating teams would meet on Tuesday ahead of another  possible meeting between Netanyahu and Gantz, hosted by the president on Wednesday, the statement said.

Likud won 31 parliament seats to Blue and White's 33 in Tuesday's election, near-complete results show.

Both parties did not win enough votes to form a majority government in the 120-seat parliament.

(With input from Xinhua, Reuters)

(Cover: A combination picture shows leader of Blue and White party, Benny Gantz (L), Avigdor Lieberman (C), head of Yisrael Beitenu party and Israeli Prime Minister Benjamin Netanyahu. /VCG Photo)