Israeli Prime Minister Benjamin Netanyahu and his main opponent Benny Gantz were called for a meeting by President Reuven Rivlin. The leaders of political parties Likud and Blue and White have agreed to explore options for a unity government. They met for the first time since last week's election.
The key meeting came as the deadlocked vote results threatened Netanyahu's long tenure in office, though he has shown no sign of being willing to give up his post.
President Reuven Rivlin ushered both men into his office in Jerusalem around 8:00 pm (1700 GMT) after shaking their hands. After roughly two hours, he left the two alone to meet before rejoining them again briefly. The trio will meet again on September 25.
Gantz and Netanyahu issued a joint statement saying that chief negotiators of the two parties would meet on Tuesday.
Rivlin, who has made clear he believes a unity government between their parties is needed to form a stable coalition, said: "We have taken a significant step forward tonight".
"The public does not want another election. They came out and voted," Rivlin said in a statement, addressing Gantz and Netanyahu.
"Now it is your turn. The responsibility for establishing a government falls on you, and the people expect you to find a solution and to prevent further elections, even if it comes at a personal and even ideological cost,” he added. Parties involved agreed not to divulge details of what was discussed. Gantz's centrist Blue and White alliance finished with 33 seats out of 120 in the September 17 elections, while Netanyahu's right-wing Likud won 31.
Both leaders might agree to head to the country on rotation as neither party has a clear party to form a majority coalition.
Gantz, says he should lead the unity government, since his party is the largest, and a compromise seems a long way off.
If the standoff goes on, there could be a third unprecedented election. The second election was called for, because, Netanyahu, despite gaining a marginal majority, was not able to form a governing coalition.
Earlier Monday, Netanyahu said, "The only government that can be formed in these conditions is a united and large one between us," Netanyahu said at a meeting of Likud lawmakers.
"The only way to reach it is to sit down and talk."
The end of the Netanyahu era would be an extraordinary moment in Israeli politics, as he has been prime minister for more than 13 years, the most in Israeli history. He also faces potential corruption charges that are pending for a hearing set for early October.
Chances for a unity government look slim as it is complicated, even though Both Netanyahu and Gantz differ marginally on important issues, like relations with the United States, the regional struggle against Iran and the Palestinian conflict.
The last time Israel saw a PM on a rotational basis was between 1984 and 1988 when Left-winger Shimon Peres and right-winger Yitzhak Shamir took turns to head the country.
The Arab bloc, The Arab Joint List alliance, the party that won 13 seats in the April election, said they were endorsing Gantz for the post of prime minister. But the decision was meant only to help topple Netanyahu's reign.
In Rivlin's consultations, Gantz received the endorsements of 54 parliament seats, while Netanyahu received 55.
Those totals do not include eight seats for ex-defence minister Avigdor Lieberman's nationalist Yisrael Beitenu party, which has endorsed neither candidate for now and could emerge as a kingmaker.
Gantz and Lieberman met on Monday, their first talks since the election.
"We exchanged opinions and viewpoints and if needed, will speak again in the future," Gantz said in a statement.
The tally also does not include three seats for one of the Arab parties that unlike the rest of the Joint List alliance, did not agree to endorse Gantz.
