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Israel's President Reuven Rivlin was set on Thursday to task parliament with forming a government to avoid new elections, after Benjamin Netanyahu and rival Benny Gantz each failed to form a coalition.

Rivlin is expected to meet Knesset speaker Yuli Edelstein Thursday lunchtime and hand him the mandate to search for a new leader.

The country's political system has been in stasis since late 2018, with two elections producing inconclusive results.

Centrist Gantz and right-wing incumbent premier Netanyahu had each been given four weeks to form a coalition by Rivlin after the second polls in September left them near neck-and-neck.

Likud leader Netanyahu attempted and failed first, with Gantz, head of the Blue and White party, admitting defeat late Wednesday.

Rivlin will now give the country's 120-member Knesset, or parliament, 21 days to find a candidate who can command a majority in the deeply divided legislature.

It is the first time in the country's history the president has been forced to take such a step.

Despite having failed in previous attempts, both Netanyahu and Gantz could be nominated.

If a candidate receives the backing of at least 61 MPs, they will have a further two weeks to form a government.

But if no candidate can gain the necessary support by 11 December, the country will hold its third elections within 12 months early in 2020.

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Netanyahu - who has been premier since 2009 but is fighting a series of corruption allegations - remains in power in an interim capacity.

The country's attorney general could announce his decision on Netanyahu's cases in the coming weeks.

'Get over the differences'

Weeks of frantic backroom negotiations will then commence, with former army general Gantz and Netanyahu still the most likely candidates.

The two men had been discussing forming a unity government alongside former defence minister Avigdor Lieberman's Yisrael Beitunu party.

Talks broke down late Tuesday, with Gantz and Netanyahu arguing over who should go first if they were to rotate the premiership.

Both have said they are open to continuing dialogue in the next three weeks.

Addressing Gantz Thursday morning, Netanyahu urged him to come to "personal, immediate negotiations, you and I, without preconditions. 

"We can get over the differences. The state is important to all of us."

Gantz on Wednesday night said he was available in the next three weeks for "direct, substantive and fast negotiations in order to establish a government that will take Israel out from the paralysis".

But Israeli media said in reality the talks were deadlocked and the parties were already preparing their campaigns for new elections.

"The 21 days left to try and spare the country from elections will most likely be filled with spin whose goal will be, for each party, to maintain its base of support - or to crush (the other party's)," Shimon Shiffer, columnist for the Yediot Ahronot newspaper, said.