Jerusalem (CNN) -- A day after thousands of Israeli demonstrators demanded an end to rules that make ultra-Orthodox Jews exempt from the draft, Prime Minister Benjamin Netanyahu said Sunday that the nation's approach to military service must change.
"The existing situation cannot continue. Neither the army, the economy nor society can continue on the current path," Netanyahu said at the start of his weekly Cabinet meeting.
The prime minister named a new team to draw up a law that would "share the burden" of military service, which is required for most Israelis when they reach the age of 18. The existing law provides an exemption for Arabs and ultra-Orthodox Jews.
The issue has been a controversial political topic for months for Netanyahu, but time is running out. Israel's Supreme Court has ruled that the law, which exempts tens of thousands of Israelis from service, must be replaced by August 1.
Such a move is sorely needed, according to thousands of protesters who marched on the streets of Tel Aviv Saturday night.
Holding banners reading, "Service for all" and "We are not suckers," they demanded a universal military draft.
More than 20,000 people turned out to protest, Israeli Police spokesman Micky Rosenfeld said.
Netanyahu acknowledged the demonstration Sunday.
"I completely understand the demand of those who serve and their families," he said.
Ultra-Orthodox students have been exempt from service through historical political agreements since Israel's establishment in 1948. Community leaders have said ultra-Orthodox men should spend their time studying the Torah at religious institutes rather than defending their country in uniforms.
Both ultra-Orthodox Jews and Arab Israeli citizens are exempt from military service. They can choose to volunteer or participate in civil service programs within their communities, but the vast majority of both groups do not participate in those programs.
The issue is a sensitive one for Netanyahu and his Likud paty, which has traditionally relied on ultra-Orthodox parties as natural coalition partners.
But his government has showed some signs of shifting toward the center. In April, Netanyahu beefed up his political dominance when he formed a coalition government with the centrist Kadima faction, bringing the number of his coalition partners to 92 in the 120-seat Knesset.
On Sunday, the Likud party approved most of the recommendations of a government committee, which had suggested changing the draft law to include ultra-Orthodox Jews. But the party said in a statement that the principle of service for all should apply to Israel's Arab population as well.
Should the Likud go ahead with its reform efforts and force thousands of Yeshiva students to join the Israeli Defense Forces, it could risk losing some of its longstanding partners.
A lawmaker from one ultra-Orthodox party criticized Netanyahu Sunday for pushing the changes, and warned that the prime minister's political alliances could be at risk.
"To my regret, Netanyahu does not understand that the demonstrators look to cut off the partnerships between us," Moshe Gafni of the Yahadut Hatorah party told Israel's army radio. "If this will be the case, Netanyahu will lose his power."
But the prime minister told his Cabinet Sunday that keeping the current system was not an option.
The previous government committee created to tackle the thorny issue dissolved due to disagreements within its members.
A new government team will draft the details of a proposed law that will be more equitable, Netanyahu said. Knesset lawmakers will have the final say.
"We are facing a historic move, a dramatic increase in the participation of the ultra-Orthodox and Arab publics in bearing the burden" Netanyahu said. "Such an increase has started, it is welcome, it is important -- but it is not enough. We want to bring about a dramatic increase in the rate of participation."
That means those who don't comply with the country's draft law should be punished, Zohara Berger-Tzur of the Israeli Forum for Equal Service told CNN.
"We demand service for all at the age of 18 and personal sanctions against those who evade duty," she said. "The new draft must comply with these demands."