Israeli Prime Minister Benjamin Netanyahu and his main rival, Benny Gantz, have claimed "significant progress" in forming an emergency government to confront the coronavirus crisis and ending the country's unprecedented political deadlock.

Gantz's 28-day mandate to put together a ruling coalition after last month's inconclusive election was due to expire at midnight on Tuesday, but President Reuven Rivlin, who is overseeing the coalition talks, extended it by two days.

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Rivlin did so, his office said, "on the understanding that they are very close to reaching an agreement".

Gantz and Netanyahu met overnight in a last-ditch effort to settle their differences. Afterwards, they issued a joint statement saying they had made "significant progress." The two are set to meet again with their negotiating teams later on Tuesday morning.

Claims of progress in coalition talks have been made repeatedly since the March 2 election, Israel's third in less than a year but a deal has remained elusive. The impasse has raised the prospect of a fourth poll, complicating any plans for economic recovery once the coronavirus outbreak eases.

In the run-up to the deadline, Gantz had urged Netanyahu to seal a deal or risk dragging the country into an unwanted election at a time of national crisis.

"Netanyahu, this is our moment of truth. It's either an emergency national government or, heaven forbid, expensive and unnecessary fourth elections during a crisis. History will not forgive either of us if we run away," he said in a nationally televised address.

Netanyahu then invited Gantz to his official residence for talks that stretched past midnight.

While last month's election ended with no clear winner, Gantz was endorsed by a slight majority of legislators, prompting Rivlin to give him the chance to form a government.

With his parliamentary majority, Gantz began moving ahead with legislation that would have disqualified Netanyahu, who has been indicted on corruption charges, from serving as prime minister in the future.

In office since 2009, Netanyahu is Israel's longest-serving prime minister and the first to be indicted while in office. He denies charges of bribery, fraud and breach of trust, filed against him in January.

Throughout three bitter campaigns, Gantz said he would never sit in a government led by Netanyahu as long as he faces corruption charges. But Gantz said the gravity of the coronavirus crisis had convinced him to change his position - a decision that drew heavy criticism from his supporters and caused his Blue and White alliance to crumble.

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The sides appeared to be close to a rotation deal in which Netanyahu and Gantz would each serve terms as prime minister.

But last week, negotiations stalled, reportedly over a demand by Netanyahu to have more influence over judicial appointments.

If their extended negotiations fail, Israel's Knesset, or parliament, will have three weeks to select a candidate for prime minister from its ranks. If that too fails, there will have to be an election.

That would mean an extended political crisis at a time when the country is dealing with its coronavirus outbreak.

Israel has reported more than 11,500 cases and at least 116 deaths from the disease, which has paralysed the economy and driven unemployment to record highs.

Netanyahu on Monday imposed a ban on inter-city travel for the final days of the Passover holiday this week to curb the spread of the coronavirus.

Restrictions already in place have confined most Israelis to their homes for weeks, forcing many businesses to close and pushed the unemployment rate to more than 25 percent.

Netanyahu said his cabinet could formulate an "exit strategy" as soon as this weekend, but he cautioned restrictions on the economy and education would be eased gradually and that there would be no full return to a routine before a coronavirus vaccine is discovered.