Political rivals of Israel's right-wing Prime Minister Benjamin Netanyahu raced on Monday to forge a diverse coalition to oust the country's longest-serving leader.

The hard-right tech millionaire Naftali Bennett was in talks with the centrist former TV anchor Yair Lapid on the terms of a "change" alliance that would end the Netanyahu era.

Israel -- after reaching a May 21 ceasefire that halted a bloody military conflict with Islamist group Hamas in Gaza -- has been thrown into fresh political turmoil.

After Israel's fourth inconclusive elections in less than two years in March, Lapid has been given a mandate to try and build a new government by midnight Wednesday.

His chances rose when Bennett declared Sunday he would join a multi-party "national unity government" in which he and Lapid would take turns to serve as premier.

Such a coalition would still need the support of other parties and lawmakers to gain a majority of 61 seats in the 120-member Knesset, Israel's legislature.

Netanyahu, in power for the past 12 years following an earlier three-year term, was fighting for his political life, warning of "a left-wing government dangerous to the state of Israel".

The 71-year-old, known as Bibi, is Israel's longest serving prime minister, and the first to face criminal charges while in office -- on fraud, bribery and breach of trust charges, which he denies.

The combative premier lashed out at Bennett, accusing him of "the scam of the century" for running on a right-wing platform but then joining a prospective government that includes liberal parties.

'Last stand'

Lapid, 57, is seeking to cobble together a diverse alliance which would include Bennett, a  supporter of Jewish settlements in the Israel-occupied West Bank, as well as Arab-Israeli lawmakers.

In order to build such an anti-Netanyahu bloc, he must sign individual agreements with seven parties, whose members would then vote in parliament to confirm the coalition.

Among them are the centrist Blue and White party of Defence Minister Benny Gantz and the hawkish New Hope party of Netanyahu's former ally Gideon Saar.

Avigdor Lieberman's pro-settlement Yisrael Beitenu party as well as the historically powerful centre-left Labour party and the dovish Meretz party would also join.

Lapid was set to speak at 2:30 pm (1130 GMT) from the Knesset, before meeting with his Yesh Atid (There is a Future) party, which has 17 seats.

Netanyahu's conservative Likud party won 30 seats in the last election on March 23, the best result of any party, but far short of a majority.

In a last-ditch bid Sunday, Netanyahu offered a three-way power sharing deal to his rivals Bennett and Saar -- but Saar refused.

Bennett accused Netanyahu of seeking to take down the political right and "the whole country with him on his personal last stand".

'Far from easy'

Lapid had mustered 51 votes of support from left, centre and right-wing parties before Bennett joined him.

Bennett's Yamina ("Rightward") party has seven seats, but one lawmaker already swore he would not cooperate with the anti-Netanyahu camp.

To win the backing of four more lawmakers, needed to achieve the required 61 seats, Lapid is counting on parties representing Arab Palestinian citizens of Israel, which have not yet announced their intentions.

They would have to support a coalition including Bennett, who previously directed the Yesha Council which represents Jewish settlers in the occupied West Bank.

"The left is making far from easy compromises here," Bennett said Sunday.

According to Israeli media, the coalition agreement would allow Bennett to head the government for the first two years, to be followed by Lapid.

It would end the long reign of Netanyahu, regarded as Israel's wiliest political survivor, who first rose to power 25 years ago on a wave of opposition to Shimon Peres, the architect of the Oslo Peace Accords.

If Lapid fails to muster a coalition, and lawmakers cannot agree on another leader, Israelis will return, yet again, to the polls.