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Gantz said in a party meeting on Monday that he would continue to work toward forging such a government, a day after sitting down with rival Netanyahu to try and put together a coalition government in the wake of two inconclusive general elections.

It was their first round of direct talks since President Reuven Rivlin on Wednesday tasked ex-military chief Gantz with trying to form a government.

Gantz said his meeting with Netanyahu touched on security, the budget deficit, but also the issues of immunity for the prime minister. Netanyahu faces graft allegations and could be indicted on corruption charges in the coming weeks.

A key point of contention in negotations is whether Gantz or Netanyahu will hold the position of prime minister first in a rotation agreement. 

Yair Lipid, from Gantz's Blue and White coalition, accused Netanyahu of seeking a third election.

"Netanyahu didn't try to build a government. I know what negotiations to build a government look like. I have seen Netanyahu, I was with him in the room when he really wanted to establish a government. He knew how it’s done," Lipid said in comments published by Haaretz.

"He didn't put any proposals on the table: He insisted on [Yakov] Litzman and [Bezalel] Smotrich. He insisted on being prime minister first in the rotation. He did everything to ensure it wouldn't work."

Following the deadlocked elections on 17 September, Netanyahu had tried to form a coalition, but finally gave up on 21 October - his second such failure this year.

A joint statement from Netanyahu's Likud and Gantz's Blue and White alliance after Sunday's meeting acknowledge they did reach any breakthrough.

"The two discussed the structure of political options available," the English-language statement said.

"Another meeting is anticipated between the two."

Earlier on Sunday the side's negotiating teams met in what Blue and White called "good spirits".

The joint statement released later said they "would continue to communicate".  

Both Likud and Blue and White say they want a unity government, but disagree on how to achieve it.

Likud has been seeking to negotiate based on a compromise set out by Rivlin that takes into account the possibility the premier will be indicted for corruption in the coming weeks.

It could see him remain prime minister for now, but step aside at some point later as he combats the charges.

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Gantz would take over as acting premier under such a scenario.

Blue and White says Gantz should be prime minister first under any rotation arrangement since his party won the most seats, finishing with 33 compared to Likud's 32.

Whoever wants to govern needs to find partners with which to control a majority of at least 61 seats in the 120-member Israeli parliament.

Agencies contributed to this report.