Speaking at the start of the Yisrael Beytenu faction meeting, Lieberman said all faction members, including Minister Sofa Landver, would vote against the proposed law.
"This is a fake law," he said. "It's a betrayal of our soldiers."
The defense minister clarified, however, that he had no intention of quitting the government before the law passed its second and third reading at the Knesset.
"I'm not volunteering to leave the government until the law's final approval," he said. "If it passes, we'll draw our conclusions."
Earlier, Prime Minister Netanyahu urged Lieberman not to quit the government.
"We have an excellent government with tremendous achievements: In the security area, in the economic area and in the diplomatic area. So it's important to continue our partnership, which is generating these tremendous achievements.
"I call on all the coalition partners, primarily Defense Minister Avigdor Lieberman, to stay in the government and continue this partnership to guarantee the State of Israel's security, prosperity and stability.
"We are facing major challenges, and we all know what they are, as well as major opportunities. It's important, therefore, to continue our partnership in a wide government which is the only way to keep serving the citizens of Israel."
Education Minister Naftali Bennett said during the Bayit Yehudi faction meeting, "This isn't just a fake crisis here. What we have here is a fake leadership which prefers to chase polls rather than tell the voters the truth and deal with it."
Addressing Netanyahu's involvement in the crisis, Bennett said: "We support the prime minister's effort. There is no deal between me and him. All the people around the table are interested in sustaining a good government."
Meanwhile, Zionist Union leader Avi Gabbay slammed the Netanyah-Lieberman "alliance of corruption," following the compromise on the IDF draft bill that was reached between Netanyahu and Deputy Health Minister Yaakov Litzman late Sunday.
"No one has any expectations from the stars of this act, Netanyahu and his defense minister. This is an alliance of corruption," Gabbay said at the start of the Zionist Union faction meeting.
"The coalition members' conduct is a spiritual weakening and moral bankruptcy. Who would have thought that they would be begging a prime minister who the police believe should be indicted for bribery? Where is your courage, integrity and leadership? We won't let Netanyahu use us to set the date that suits him best. We will do what's good for Israel."
Hatnua leader Tzipi Livni said during the meeting, "This is the beginning of the end for the prime minister, the government and their political path. This is also a fascinating example of what this government symbolizes, with the radicals leading Netanyahu by the nose. The prime minister, who leads the biggest party, has no stand. All he has are survival considerations."
She warned that the IDF draft law was illegal and unconstitutional.
At the Yesh Atid faction meeting, party leader Yair Lapid said that the compromise on the "draft-dodging law" proved "just how cynical, rotten and shameless our politics is.
"According to the draft-dodging law," Lapid added, "if they don't feel like enlisting—there's no problem. This law is an insult to the IDF and an insult to those who enlist. The political system around us is losing all its values."
Ministerial committee approves draft bill
The new IDF draft bill accepted by the Hasidic Council of Torah Sages was approved by the Ministerial Committee for Legislation on Monday morning and will be sent to a preliminary Knesset reading Wednesday.
One of the members of the ministerial committee, Immigration Absorption Minister Sofa Landver of the Yisrael Beytenu party, didn't show up for the vote but left a note stating her objection to the bill.
Following the vote, Landver filed an appeal against the bill's approval, requiring the committee or the government to reconvene to cancel the appeal.
Senior Justice Ministry officials said Monday that the new draft bill approved by the Hasidic Council of Torah Sages failed to meet the rules and conditions presented by the High Court of Justice for an equal share of the burden. Attorney General Avichai Mandelblit told Justice Minister Ayelet Shaked before the vote that there is a constitutional obstacle to advance the law as it contradicts the equality value. Nevertheless, Shaked plans to send the bill to a preliminary Knesset reading, assuming the problem will be dealt with at a later stage.
According to the Justice Ministry officials, once the coalition factions and the prime minister reach a final decision on an acceptable draft bill, it will seen as a governmental bill and the attorney general would provide his final opinion pertaining to whether it meets the conditions for an equal share of the burden, as formulated by the High Court.
The bill is based on a framework put forward by Shas MK Yoav Ben-Tzur, which states that a goal will be set of 3,800 Haredi recruits joining the IDF and national service with each recruitment cycle—with their number gradually increasing.
In addition, the law will omit any sanctions or incentives, instead including an article starting that the government will inspect general draft quotas every five years and if it finds Haredi conscripts failed to meet them, the law will expire.