Israelis faced the growing possibility of a new national poll despite a general election last month.
It comes as Prime Minister Benjamin Netanyahu's coalition talks remained deadlocked ahead of a looming deadline.
Mr Netanyahu, who risks a major setback if he fails to reach an agreement before Wednesday night's deadline, spoke in Israel's parliament and said it was still possible a deal could be brokered to avoid "unnecessary" elections.
But he spoke shortly after parliament took the first step towards holding new polls, by preliminarily approving a law to dissolve itself.
Israeli President Reuven Rivlin (R) shakes hands with Israeli Prime Minister Benjamin Netanyahu (L). Source: EPA
Three more rounds of voting are needed for final approval.
Earlier in the day as Netanyahu failed to convince a right-wing party leader to compromise and allow a deal to be reached, his close ally US President Donald Trump offered his support.
"Hoping things will work out with Israel's coalition formation and Bibi and I can continue to make the alliance between America and Israel stronger than ever. A lot more to do!" Trump, currently visiting Japan, said on Twitter, using Mr Netanyahu's nickname.
Ex-defence minister Avigdor Lieberman has prevented a deal by refusing to budge from a key demand, and he showed no sign of backing down.
Holding elections so close to one another would be unprecedented in Israel, and there have been concerns over the cost and prolonged political paralysis that would result.
Ex-defence minister Avigdor Lieberman has prevented a deal by refusing to budge from a key demand. Source: AAP
Mr Netanyahu sought to place full blame on Mr Lieberman, who rejected the assertion.
"There's no reason to drag the country to unnecessary elections that will cost a fortune and paralyse us all for another half a year," Mr Netanyahu said in his address in which he also referenced Mr Trump's tweet.
'Matter of principle'
Mr Lieberman said he had already made concessions and was not prepared to go further, adding he was ready for new elections if needed.
The former defence minister is seeking a guarantee that legislation he supports aimed at having ultra-Orthodox Jews perform mandatory military service like other Jewish Israelis be approved without changes.
His party controls five seats in parliament and Mr Netanyahu needs his support for the coalition he is seeking.
"It's a matter of principle," Mr Lieberman told journalists, calling Mr Netanyahu's inability to form a government a "huge, unprecedented failure."
The issue of military service for ultra-Orthodox Jews is a highly sensitive one in Israeli politics and the bill is opposed by ultra-Orthodox parties, who control 16 seats in parliament and are also slated to form part of Netanyahu's coalition.
April elections left Mr Netanyahu's Likud party along with its right-wing and religious allies with 65 of 120 seats in parliament, putting him in position for a fifth term and on track to become Israel's longest-serving premier later this year.
He is at the same time facing possible indictment for fraud, breach of trust and bribery in the months ahead.
A pre-indictment hearing is expected to be held in early October, and there have been reports that Mr Netanyahu is seeking legislation in the new parliament that could result in him being granted immunity from prosecution.
If a coalition deal is not reached by Wednesday night's deadline, Israeli President Reuven Rivlin could give Mr Netanyahu another two weeks if he concludes the premier is the only person capable of forming a government.
Alternatively, Mr Rivlin could ask another member of parliament to form a government.
Mr Netanyahu is widely seen as preferring new elections rather than leaving the choice up to Mr Rivlin, due to the possibility someone else could be selected.
Mr Netanyahu could also seek to form a minority government.
