"If Netanyahu doesn't keep his promises, then the crisis is going to be severe and there won't be a partnership," Mofaz told the Yediot Ahronot daily.
The exemptions have become a major point of division in Israeli society.
Under a long-standing arrangement, ultra-Orthodox seminary students are permitted to skip mandatory military service to pursue religious studies.
This system, begun six decades ago by Israel's founding fathers, was meant to allow several hundred gifted scholars to revive institutions of Jewish learning after the killing of six million Jews in the Holocaust.
The numbers of exemptions have swelled over the years, and today, more than 60,000 young religious men are exempt from military service.
These exemptions, combined with a refusal to enter the workforce and a sense that they are trying to force their strict religious mores on the general public, have bred resentment among Israel's secular majority, where men are required to serve three years in the military and women just under two years. Many must serve additional decades as reservists.
Modern Orthodox Jews, who make up about 15 percent of the Jewish population, serve in the military.
Earlier this year, the Supreme Court ruled the system illegal and gave the government until Aug. 1 to formulate a law.
Netanyahu put Kadima in charge of a parliamentary committee created to draft the legislation. On Monday, he disbanded the committee over deep disagreements among members.
Ultra-Orthodox parties oppose any change in the system and refuse to cooperate with the committee. Two other parties quit the panel because the new law might not apply to Israel's minority Arabs, who also do not serve in the military.
Mofaz said the disbanded committee would still issue its recommendations Wednesday. He said if Netanyahu did not take the "necessary step" of using the report as the basis for a new draft system, "the national unity government will come to an end."
An Israeli official, speaking on condition of anonymity, said that Netanyahu was working to resolve the standoff.
He said Netanyahu remained committed to key principles worked out with Kadima: Ensuring that all sectors of Israeli society share the burden of military and national service, implementing any changes gradually, and maintaining national unity.
Officials have said they expect a final compromise to reduce, but not eliminate, draft exemptions for the religious and create some sort of civilian national service for Israeli Arabs.