Should he eventually form a formal coalition government, critics fear he will use his office to push through a law that would grant him legal immunity. Mr. Netanyahu rejects the claim, but has promised legal reforms that would limit the role of the Supreme Court.

Mr. Rivlin now takes center stage: He must consult with each of the 13 parties elected to Parliament before formally asking a political leader to try to form a majority coalition, an invitation that is likely to be made in 10 days.

Israeli presidents have typically offered this right to the leader of the largest party, which in this case would be Mr. Netanyahu, whose Likud party won 30 seats.

But Mr. Rivlin has the right to offer it to any lawmaker he deems best able to form a coalition, which in this case might be Mr. Lapid.

Whoever receives the invitation is expected to struggle to form a coalition. If Mr. Netanyahu persuades Raam to join his coalition, he could lose the support of a far-right alliance already in his bloc. That alliance, Religious Zionism, said Thursday that it would refuse to serve in a government supported by Raam.

Similarly, Mr. Lapid may struggle to persuade two right-wing parties within his alliance to sit not just with Raam, but with another Arab group called the Joint List.

And even if either leader somehow does form a coalition, it is expected to be so fragile and ideologically incoherent that it would struggle to last longer than a few months.

Irit Pazner Garshowitz contributed reporting.

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