Israel's president warned on Sunday that the country faced an "historic constitutional crisis" over a contested judicial reform plan, and said he was mediating between the relevant parties.

Prime Minister Benjamin Netanyahu, now in his sixth term, wants to rein in the Supreme Court, which members of his religious-nationalist coalition accuse of overreach and elitism.

Opponents of the plan, who held nationwide protests on Saturday, say it would cripple judicial independence, foster corruption, set back minority rights and deprive Israel's courts of credibility that helps fend off war-crimes charges abroad.

"We are in the grips of a profound disagreement that is tearing our nation apart. This conflict worries me deeply, as it worries many across Israel and the (Jewish) Diaspora," President Isaac Herzog said in a statement.

Herzog, whose post lacks executive powers and is designed to unify an often fractious Israeli society, said he was "working full time, by every means, making nonstop efforts with the relevant parties, with the aim of creating wide-reaching, attentive, and respectful discussion and dialog."

"I am now focused on ... two critical roles that I believe I bear as president at this hour: averting a historic constitutional crisis and stopping the continued rift within our nation."

In televised remarks at his weekly cabinet meeting, Netanyahu made no mention of Herzog's overture.

Judicial reforms, he said, had been sought by previous governments of various political stripes "and no one then thought about talking about an end to democracy."

Promising a "delving discussion" in a parliamentary review committee where the opposition has representation, Netanyahu said: "We will complete the reform legislation that will fix what needs fixing, will fully protect individual rights and will restore the public's trust in the justice system."

Yair Lapid, centrist head of the opposition, was dismissive of such assertions, telling Ynet TV: "They (the coalition) are pretending that this is a constitutional issue."

But he also expressed openness to a measure of reform.

Whereas Netanyahu wants to empower the 120-seat Knesset to override some Supreme Court rulings with a 61-vote majority, Lapid suggested raising that threshold to 70 votes - including 10 opposition lawmakers. Netanyahu's coalition controls 64 seats.

Lapid also proposed a referendum: "It would be reasonable to go and consult with the people before deciding to turn democratic Israel into non-democratic, no?"