JERUSALEM — Israeli President Reuven Rivlin summoned Prime Minister Benjamin Netanyahu and his chief rival Benny Gantz to a joint meeting Monday night in hopes of brokering a deal that would weld their two bitterly divided parties into a unity government.

The three met for almost two hours at the president’s official residence, with Rivlin eventually leaving the competitors to talk alone. 

The two party leaders issued a joint statement afterward, saying, “Following the president’s appeal, Prime Minister Benjamin Netanyahu and the chairman of the Blue and White party of Gantz, discussed ways to advance Israel’s unity and agreed that the leaders of the two parties would meet tomorrow.”

The statement added that Rivlin had invited the two men back to the presidential residence on Wednesday for another meeting.

“We have taken a significant step forward tonight, and now the first challenge is to establish a channel of direct communication between the sides,” Rivlin said in a statement after the meeting. The three had agreed not to reveal the nature of the conversation “at this time,” the statement said. 

The discussions come as the country waits for Rivlin to kick off the next phase of Israel’s protracted political process: to announce which candidate he has chosen to make the first attempt at forming a governing coalition. Over the past two days, all nine parties that won seats in the election last week made recommendations to Rivlin, and he could make his pick at any time. 

Gantz and Netanyahu are fiercely jockeying for advantage. But the president has made it known he would like to see the two major parties work together in the next government, possibly with Gantz and Netanyahu each taking a turn as prime minister. 

As is often the case in Israeli politics, the complications are dizzying. Netanyahu is facing likely indictment on corruption charges, and he could boost his chances of avoiding prosecution if, in a unity government, he gets the first turn as prime minister. Gantz has pledged never to serve in a coalition with Netanyahu’s Likud party unless someone other than Netanyahu is in charge.

Gantz’s party won two more seats in the Knesset, or parliament, than Likud, leading many analysts to predict that he would get the first chance to form a government. But Likud was recommended by 54 members of the Knesset, one more than Gantz’s Blue and White party.

Rivlin’s call for a face-to-face meeting led some to hope that a breakthrough would be possible, paving the way for a coalition government and avoiding a third election in a year.

“Israelis will feel that if anyone can find a solution, it’s President Rivlin,” said Jason Pearlman, a former media adviser to Rivlin. “He wants to sit them down and let them sort it out.” 

Last week’s vote, the second in less than five months, left the two leaders, their parties and their natural ideological blocs nearly equally split. Neither side has the minimum of 61 seats out of Israel’s 120-seat parliament to establish a stable government.

The usual horse-trading among factions seeking to join a governing coalition was roiled Sunday when a group of Arab parties agreed to back Gantz. It was the first time in almost three decades that the Arab legislators broke with a long-standing boycott of Israel’s government-forming process. Leaders of the group, known as the Joint List, said they were motivated by what they view as Netanyahu’s racial incitement against Arab Israelis — about 20 percent of the population — during the campaign, painting them as an enemy and a danger to the country’s stability.

A new poll found that three out of four Arab citizens of Israel favor their representatives’ participation in a government coalition. Nearly half of the country’s Jewish citizens oppose Arab participation.

In a tweet Sunday, one of the party’s key leaders, Ahmad Tibi, wrote, “Today history will be made: We’ll do what we need to bring down Netanyahu.”

When making a recommendation, the leader of the Joint List, Ayman Odeh, told Rivlin that supporting Gantz, a retired lieutenant general, was the hardest thing he had ever done. Gantz, then chief of the Israeli army, led Israel’s 2014 war with the Islamist group Hamas and other militant Palestinians in the Gaza Strip. Acting on his orders, Israeli forces devastated large parts of the Palestinian enclave, killing about 2,000 people, mostly civilians. Three Arab parliamentarians from the Balad party later backed out of supporting Gantz, one of them calling him “a war criminal.”

Netanyahu condemned the Join List’s endorsement, and Blue and White members distanced themselves from it. 

Avigdor Liberman, the nationalist party leader who blocked Netanyahu’s attempt to form a government after April’s election, abstained from recommending either candidate, saying he supports neither a government with the Arab legislators who backed Gantz nor one with the ultra-Orthodox religious parties that form part of Netanyahu’s coalition.

Liberman has pressed for a coalition between Blue and White and Likud that would squeeze out any need to include the small, fringe factions. He called on both leaders to put aside their egos and join forces.

“For now, we are happy to remain in the opposition,” said the Moldovan-born former nightclub bouncer. His abstention in this phase of the protest does not rule out his participation in a coalition at a later stage. 

Gantz has remained largely silent, sticking to his campaign promise not to form a government with Netanyahu because the incumbent faces a series of impending criminal indictments. Netanyahu is set to meet with the attorney general next week for a hearing on three cases of fraud, bribery and breach of trust. Gantz previously spurned an invitation to meet face to face with Netanyahu, while saying he would be willing to enter a unity government with Likud, but only under his own leadership

Netanyahu called Thursday for a meeting with Gantz to discuss a power-sharing arrangement, but he did not indicate whether he would be willing to cede power to Gantz or even rotate the leadership with his political rival, whom he has accused of being too weak and inexperienced. 

Whoever Rivlin chooses to have a first chance at forming the next Israeli government will be given 28 days, plus a 14-day extension, to secure coalition agreements. If that candidate fails, the president can permit a further 28 days. After that, Knesset members would have an opportunity to recommend, by majority vote, a third potential candidate they believe might be successful. That person would then have 14 days to try to form a government.