Israel's PM Benjamin Netanyahu has warned that a proposed unity government aimed at replacing him would be a danger to the country's security.
He urged fellow right-wingers not to back a deal after ultra-nationalist Naftali Bennett said he would form a coalition with a centrist party.
Mr Netanyahu's opponents have until Wednesday to form a government.
If they are successful, it would bring to an end the rule of the country's longest-serving prime minister.
Mr Netanyahu, who faces serious corruption charges and could go to jail, fell short of a decisive majority at a general election in March. It was the country's fourth inconclusive vote in two years - and again he failed to secure coalition allies.
But his opponents may only be able to form a minority government, propped up by Arab members of parliament.
On Monday, the centrist opposition leader Yair Lapid warned that "many obstacles" remained before a unity government could be formed.
"We'll have to overcome them together," he told journalists. "That's our first test - to see if we can find smart compromises in the coming days to achieve the greater goal."
Tensions remain following the recent Gaza conflict, which also triggered inter-communal clashes in Israeli cities between Jews and Arabs.
Some Arab politicians could be reluctant to back a government led by Mr Bennett, who is a staunch supporter of Jewish settlement in the Israeli-occupied West Bank - land Palestinians want for a future state.
'Fraud of the century'
"Don't form a left-wing government - such a government is a danger to Israel's security and future," 71-year-old Mr Netanyahu, who has dominated Israeli politics for a generation, said on Sunday.
Naming left-wing leaders who, he hinted, could weaken Israel's security cabinet, he asked: "What impact will that have on Israel's deterrent capability? How will we look to our enemies? What will they say in Iran and Gaza?"
Mr Netanyahu accused Mr Bennett of "misleading the public" and of carrying out "the fraud of the century" - a reference to the Yamina party leader's previous public promises not to join forces with Mr Lapid.
Mr Bennett, 49, earlier announced in a televised address that his party would join talks to form a unity government.
"Mr Netanyahu is no longer trying to form a right-wing government because he knows full well that there isn't one. He is seeking to take the whole national camp, and the whole country, with him on his personal last stand," Mr Bennett said.
"I will do everything to form a national unity government with my friend Yair Lapid."
Before the announcement, Israeli media reported that under the proposed terms of the deal, Mr Bennett would replace Mr Netanyahu as prime minister and later give way to Mr Lapid, 57, in a rotation agreement. The arrangement has not been officially confirmed.
The proposed coalition would bring together factions from the right, the left and the centre of Israeli politics. While the parties have little in common politically, they are united in their desire to see Mr Netanyahu's time in office come to an end.
Mr Lapid, a former finance minister, was given until 2 June to form a new coalition government after Mr Netanyahu failed to do so. His Yesh Atid party came second to Mr Netanyahu's right-wing Likud at the last election.
Netanyahu fights on
After an evening of high political drama on Sunday, Israel is much closer to a new coalition that will unseat its long-time prime minister. But Benjamin Netanyahu should not be written off.
He was quick to respond to the latest announcement with his own appeal to right-wing members of Naftali Bennett's Yamina party - and those of Gideon Saar's New Hope - not to join the agreement.
He taunted them by asking "Who will take care of settlements?" and suggested the proposed unity government would offer a weak security cabinet that would be unable to stand up to Israel's rival, Iran.
If he chips away just a couple of members of parliament with these attacks, then the prospective government could tumble.
And even if this coalition does get sworn in, it will be a fragile one - bringing together parties from across the political spectrum with stark ideological differences. To stay in power, it will be forced to kick many sensitive issues into the long grass.
On Saturday night, Mr Netanyahu's Likud party made an offer to Mr Bennett and the leader of another potential coalition party to share the premiership in a three-way split.
His offer was rejected but the prime minister repeated the same option on Sunday.
Under Israel's electoral system of proportional representation, it is difficult for a single party to gain enough seats to form a government outright. Smaller parties are usually needed to make up the numbers needed for a coalition.
Mr Lapid was initially given a 28-day mandate to form a government but this was interrupted by the recent 11-day conflict in Gaza.
One of his potential coalition partners, the Arab Islamist Raam party, broke off talks because of the violence.