Mr. Rivlin seemed to acknowledge as much, saying he was handing the mandate to form a government to Mr. Netanyahu because his chances were greater than Mr. Gantz’s “at the moment.”

Mr. Gantz won the endorsements of only 54 lawmakers, one shy of Mr. Netanyahu’s total, but 10 of them were from Arab lawmakers who said they would not join a Gantz government. Mr. Rivlin apparently discounted those endorsements for that reason.

But eight days after the election, it could still play out in any number of ways, taking Israel’s future with it.

Mr. Netanyahu could tempt his former ally turned rival, Avigdor Liberman, leader of the secular, ultranationalist Yisrael Beiteinu, which won eight seats, back into a partnership. Mr. Liberman has said he would refuse to join a coalition with Mr. Netanyahu’s ultra-Orthodox coalition partners, but perhaps, some analysts said, he would renege on his election promises, citing the good of the country.

Mr. Rivlin had been pushing Mr. Netanyahu and Mr. Gantz to forge a broad unity government including both their parties, saying that was the will of the voters. And on Wednesday, Mr. Netanyahu said a unity government was the only way out of the political stalemate.

“Neither of us can form a government other than with each other,” Mr. Netanyahu said. And after a difficult election campaign, he said, a unity government was essential “to achieve national reconciliation.”

A unity government could set the country on a more moderate, unifying path after years of increasingly polarizing right-wing and religious governments.