Benjamin Netanyahu reached out to his rival to join hands, but the latter said that he would be PM.

Israel's president will meet both Prime Minister Benjamin Netanyahu and his main opponent Benny Gantz on Monday evening as he pressures their two parties to form a unity government, his office said.

President Reuven Rivlin announced in a statement he had invited the two to a meeting together as he considers whom to task with trying to form a government following last week's deadlocked elections.

Rivlin made the announcement after he wrapped up consultations with political parties elected to parliament to hear their recommendations for who should form the next government.

Gantz's centrist Blue and White alliance finished with 33 seats in the September 17 elections, while Netanyahu's right-wing Likud won 31.

Despite Gantz's slim lead, neither has a clear path to a majority coalition, putting Netanyahu's long tenure in office at risk.

Both Netanyahu and Gantz have also called for a unity government.

Gantz however says he should lead it since his party is the largest.

The standoff has even raised the possibility of yet another election -- which would be the third in a year's time after April polls also ended inconclusively.

Rivlin has said he will do all he can to avoid another election, and Monday's meeting may see him seek to play a mediator role.