That could open the way for Netanyahu's rival and former military chief Benny Gantz, leader of the centrist Blue and White party, to try.
The point of contest resolves around Lieberman's refusal position to not move an inch off the proposed stricter draft law that would increase the number of Orthodox males to serve in the army.
All it would take, according to conventional wisdom, was the usual wheeling and dealing on cabinet posts and allied factions' pet projects.
"A lot can be done in 48 hours", he said. The move comes as a deadline to form a coalition government nears with no progress in sight. "The voters' wishes can be respected, a strong right-wing government can be formed". If Netanayhu does not announce a new government by then, President Reuven Rivlin can choose another legislator to form a government.
If efforts to break the political deadlock fail, parliament would take a final vote on an election on Wednesday.
It could mean bad news for Netanyahu.
Lieberman is seeking a guarantee that legislation aimed at having ultra-Orthodox Jews perform mandatory military service - like other Jewish Israelis - be approved without changes.
But political commentators said it was still unclear if Netanyahu could muster the required 61 votes to pass the motion.
The issue is highly sensitive in Israel and the legislation is opposed by ultra-Orthodox parties, who control 16 seats in parliament and are set to become a key member of Netanyahu's coalition.
Netanyahu is widely seen as preferring new elections rather than leaving the choice up to Rivlin, due to the possibility someone else could be selected.
"We are not looking to bring down Netanyahu and we are not looking for an alternative candidate to support, but we will not give up our principles and promises to the citizens of the State of Israel", he said.
Avigdor Lieberman, the president of the political party Israel Beiteinu is still holding back the 5 seats that his party won 5 in this years election. Witkon's ruling continued: "Anyone who saw this during the days of the Weimar Republic [the German government from 1918-1933 which gave rise to the election of Nazi leader Adolf Hitler] will not forget this lesson".
"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", Trump tweeted on Monday.
Both leaders have been in lockstep over policy towards the Palestinians, who have accused Trump of being partial towards Israel, and Iran.
How would an election affect Netanyahu's legal predicament?
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