Benjamin Netanyahu, rival party leader Benny Gantz hold talks to break Israel's political deadlock following inconclusive election last month

Jerusalem: Israel's prime minister and his main rival opened a new round of unity talks on Sunday in the latest effort to break a political stalemate and avoid an unprecedented third parliamentary election in less than a year.

Israel has been paralyzed by political deadlock following an inconclusive election last month, with neither prime minister Benjamin Netanyahu's Likud nor the rival Blue and White party in control of a 61 seat majority in parliament.

File image of Israeli prime minister Benjamin Netanyahu. AP

After nearly a month of efforts, Netanyahu last week said he had failed to cobble together a coalition. Israel's president has now given the task to Blue and White party leader Benny Gantz. Gantz, a former military chief, met with Netanyahu in Tel Aviv to discuss a possible power-sharing agreement.

Gantz's party issued a statement that the two discussed possible options and agreed to a second meeting. Ahead of the talks, Netanyahu expressed support for a "broad national unity government." Speaking to his Cabinet, Netanyahu said such a coalition is essential for Israel to face what he said were mounting security challenges around the region.

"We must make tough decisions that require a government with broad shoulders," he said. "This is not a political question, but a national and security question of the highest order. I hope that we can advance this goal in the coming days."

With Blue and White controlling 33 seats in parliament and Likud holding 32, the two parties together have enough support to form a government together. While both men support the idea of a unity deal, they have disagreed over who should lead it.

Netanyahu wants his traditional religious and nationalist allies to sit with Likud and Blue and White. Gantz has been cool to sitting together with Netanyahu's hardline allies. He also refuses to serve under a Netanyahu-led government while the long-serving leader faces possible indictment for corruption charges.

Israel's attorney general is to decide on whether to charge Netanyahu in the coming weeks. Ahead of their meeting, negotiators from the two parties met for preparatory talks that were "held in good spirits," according to a Blue and White statement.

It is the first time in more than a decade that a candidate other than Netanyahu has been given the opportunity to form a government. But without Likud, Gantz's options are limited. He can try to break up Netanyahu's right-wing bloc and win over smaller hard-line parties. So far, there is no sign of that happening.

His remaining potential partners include a diverse group of parties that have little in common, including the secular ultranationalist Yisrael Beitenu party, dovish Jewish parties and a grouping of Arab parties, which have never sat in a government before.

The country has faced political paralysis since Yisrael Beitenu leader Avigdor Lieberman refused to sit in a government with Netanyahu's ultra-religious partners following April's election. That decision robbed Netanyahu of a parliamentary majority, leading to last month's inconclusive election.

Lieberman has refused to endorse either candidate for prime minister and demands they reach a unity deal. If the sides fail, Israel could face a third election early next year.