Israeli PM Benjamin Netanyahu is set to meet his finance minister on Sunday, in what is being seen as a last-ditch attempt to avert early elections.
Moshe Kahlon’s Kulanu party is vital to the coalition’s survival.
The talks come ahead of the weekly cabinet meeting, and amid a political crisis triggered by the defence minister’s resignation on Wednesday.
Talks between the PM and another coalition rival to find a way forward ended without agreement on Friday.
Naftali Bennett has threatened to pull his party Habayit Hayehudi out of the governing coalition if he was not appointed the new minister of defence.
Former Defence Minister Avigdor Lieberman quit in opposition to Israel’s decision to accept a ceasefire with militants in the Gaza Strip after three days of intense violence last week.
What has triggered this?
The withdrawal of Mr Lieberman and his Yisrael Beiteinu party left the coalition with just a one-seat majority in the knesset (parliament).
Mr Bennett’s Habayit Hayehudi is the third-largest party in Prime Minister Benjamin Netanyahu’s coalition, and if he pulls out Mr Netanyahu will be left with an unworkable minority.
While Mr Bennett has called for early elections, Mr Netanyahu opposes them.
Mr Kahlon has also said he does not think the coalition can continue.
Under the law, elections are not due until November 2019 at the latest.
If elections are called, what will it mean?
The current government has been in power since March 2015. It has been described as the most right-wing in Israel’s history, comprising mostly nationalistic and religious parties which take a hard line towards dealing with the Palestinians and reject the notion of trading occupied land for peace.
All Israeli governments are coalitions because of Israel’s system of proportional representation, meaning no single party can govern alone.
Although Mr Netanyahu does not want to call early elections, recent polls show he is still a favourite to be prime minister among the electorate, and his Likud party has the most support.
However, even if Likud remains the largest party, that does not necessarily mean it will stay in power if other parties can form a coalition without it.
Mr Netanyahu has won four elections and if he remains in office past 31 May 2019 he will surpass Israel’s founding father David Ben-Gurion as the country’s longest-serving prime minister.
What led to the crisis?
Last Sunday, an undercover Israeli unit was intercepted in Gaza, which is run by the Palestinian militant group Hamas.
An ensuing firefight, which saw Israel tanks and aircraft open fire, left seven Palestinian militants and one of the Israeli commandos dead.
Hamas unleashed some 460 rockets and mortars at Israel over the next 48 hours – the heaviest barrage since the two sides fought a war in 2014. Israel responded with 160 air strikes, targeting militant sites in Gaza.
The violence killed seven more people in Gaza and one in Israel.
On Tuesday, Hamas and Israel agreed to cease fire after Egyptian mediation.
Avigdor Lieberman, and Mr Bennett, both opposed Israel’s decision, seeing it as a surrender. Mr Lieberman said it made his position untenable, while Mr Bennett demanded to become defence minister “so that Israel will go back to winning”.