JERUSALEM — Prime Minister Benjamin Netanyahu vowed Sunday to increase significantly the number of ultra-Orthodox Jews and Arab citizens who serve in Israel’s military or civilian volunteer corps, an effort that he hoped would quiet an outraged public and save his broad unity coalition government.

A week after disbanding a committee he had appointed to address the issue of draft exemptions, Netanyahu embraced the committee’s core ideas. He appointed its chairman, a member of Parliament from the centrist Kadima Party, and one of the top ministers from his more conservative Likud Party to work out the details of a new conscription law.

The goal is to have the Cabinet approve the legislation by next Sunday so Parliament can act on it before an Aug. 1 deadline to replace the existing law that exempts thousands of yeshiva students from serving in the military. That law was struck down by the Supreme Court in February.

The issue has fueled resentment over how national burdens are shared and has exposed social divisions.

“We are citizens of one state, and we must all participate in bearing the burden of service to the state,’’ Netanyahu said Sunday at the start of his Cabinet meeting, according to a statement released by his office.

The prime minister called for ‘‘historic change’’ and promised incentives for those who serve and sanctions against those who do not.

The move came hours after a protest in Tel Aviv on Saturday that drew about 20,000 people demanding a broader military draft and the resignation of several politicians. It also followed a week of political turmoil in which several important members of Netanyahu’s coalition threatened to quit over the issue. For now, the political crisis seems to have been contained.