"I call on all the coalition partners, and chief among them Defence Minister Avigdor Lieberman, to remain in the government and continue this partnership in order to ensure security, prosperity and stability for the State of Israel", he said. "The bill as presented is what is called a classic 'fake law, '" he said at his faction meeting.
They have threatened retaliation: If the bill does not pass, the parties said they won't vote to approve the country's 2019 budget, which both Netanyahu and Economy Minister Moshe Kahlon, head of the Kulanu party, have identified as a high priority.
On Sunday, Netanyahu said that the precedent set by Iran could end up "nuclearizing the Middle East" and prompting a risky arms race.
In a letter to Edelstein, Meretz MK Tamar Zandberg and Yesh Atid MK Ofer Shelach argued that a dissolution bill should be given the same privileges as the ultra-Orthodox conscription bill, which the coalition is planning to vote on this week.
At a meeting on Sunday, influential rabbis reportedly chose to stick by the demand that a bill on the military exemption be approved before the budget is passed while rejecting compromise legislation that had been proposed.
"We'll vote against the enlistment law", he pledged.
"If there are elections, we will contend and win, but we are not there yet. The hour is late, but not too late", he said, above heckles from the opposition.
Yisrael Beiteinu is mostly comprised of immigrants from the former Soviet Union who came to Israel by the hundreds of thousands after the collapse of the Iron Curtain. "We need to make one last supreme effort to preserve the longevity of this government in its current form".
Although Lieberman has enjoyed a healthy working relationship with Netanyahu and his similarly conservative Likud party, a schism has persistently existed in the coalition between secular parties like Yisrael Beiteinu and orthodox parties like The Jewish Home, Shas and UTJ.
Opposition politicians and a leading member of the prime minister's coalition have accused Netanyahu, who is polling strongly of seeking snap elections as a way to bolster his standing in the event of a criminal indictment.
Netanyahu, 68, could soon face charges in at least two separate corruption affairs. "Therefore, it is important to continue the partnership between us with a broad government as only it can continue to serve the citizens of Israel", he added.