The crisis, which could spark early elections, came after ultra-Orthodox parties said they would not support the 2019 state budget unless the draft exemption legislation is approved.
The threat to the coalition comes mainly from the quarrel between the secular Yisrael Beiteinu party and the ultra-Orthodox Shas and United Torah Judaism (UTJ) concerning military draft legislation.
Some coalition partners accuse Netanyahu of wanting early elections to bolster his political standing ahead of his possible indictment for bribery in the coming months.
Coalition members, including Lieberman's Yisrael Beitenu party, will be able to vote against the conscription bill, but that will likely not be enough to prevent its approval.
Finance Minister Moshe Kahlon said he would resign if the budget did not pass in the Knesset's winter session, which ends on Sunday.
"I said that the nuclear agreement with Iran contains within it many dangers for the world, including the special danger of the nuclearization of the Middle East", Netanyahu said, according to a statement released on his behalf.
If new elections are called, however, Bennett vowed to back Netanyahu for the premiership, and predicted his Jewish Home party would be the "dominant" coalition partner in the next government.
Gorton MP receives suspicious package a time Westminster office
It emerged today that two more suspicious packages have been sent to the Houses of Parliament, with another man taken to hospital. Huq said she had been assured that the substance was not harmful, but told the BBC that the parcels were now "part of a pattern".
Right-wing and religious parties in the government are divided over the framing of a bill that would protect the exemption ultra-orthodox men have traditionally enjoyed from compulsory military service.
The need for a new bill arose after the Supreme Court in September struck down a law allowing ultra-Orthodox men to be exempted from military service up until 2023.
The bill is set to be put to the vote in the Knesset (parliament) plenum later in the day, where it needs three full rounds of votes to become a law.
Israel's defence minister said Monday he would remain in the government for now, leaving Prime Minister Benjamin Netanyahu's coalition intact after intensifying speculation over whether the country is headed for early polls. However, to date, he has not done so and even instructed Absorption Minister Sofia Landver to vote against the bill when presented to the Ministerial Legislative Committee instead of absenting herself or abstaining. "We don't want elections and we don't want the government to break up, but not at any price".
Police have already recommended Netanyahu be charged in two corruption cases.
Israeli Prime Minister Benjamin Netanyahu addressed the lawmakers as part of the Tuesday evening discussion.
He is not required to step down if indicted - only after he is convicted with all appeals exhausted - though political pressure would surely mount.