Benny Gantz, the chief political rival of Prime Minister Benjamin Netanyahu, said Wednesday that he had failed to form a new government ahead of a looming midnight deadline, propelling a deeply divided Israel into a new, uncharted phase of political chaos and increasing the likelihood of a third election in a year.

In a statement on Wednesday evening. Mr. Gantz’s Blue and White party said he had informed Israel’s president, Reuven Rivlin, that he had been unable to form a government.

Israel has been gripped by political paralysis since April, when the first of two inconclusive elections was held. The second took place in September.

In both elections, Mr. Gantz and Mr. Netanyahu emerged neck and neck, each falling well short of a majority. Each was given a chance to assemble a majority coalition and failed.

At this point, there is no guarantee that a third vote would produce a significantly different outcome.

The charge of forming a government now goes to Israel’s Parliament, which will have 21 days to come up with a candidate — any candidate, including Mr. Netanyahu or Mr. Gantz — who could command a majority of 61 seats in the 120-seat house.

The Blue and White statement said that Mr. Gantz “will continue his efforts over the next 21 days to form a good government for the citizens of Israel.”

If that final stage, which Israel is entering for the first time in its history, also fails to produce a government, Parliament would be dissolved and Israel would start preparing for its next election, most likely in the spring.

Both Mr. Netanyahu, Israel’s longest-serving prime minister and leader of the conservative Likud, and Mr. Gantz, a centrist and relative political newcomer, have said they wanted to join forces in a broad government of national unity based on their two large parties.

But they have failed three times to agree on a power-sharing arrangement.

The negotiations have been complicated by, among other things, Mr. Netanyahu’s legal situation. He is facing possible indictment in three graft cases involving allegations of bribery, fraud and breach of trust.

Israel’s attorney general, Avichai Mandelblit, is expected to announce his decision on charges against Mr. Netanyahu by the end of the month.

Mr. Gantz has said he would join a unity government with Likud, but that he would not serve under a prime minister facing indictment. Likud has insisted that Mr. Netanyahu is its leader and has refused to entertain the idea of a governing coalition without him.

Recent talks have focused on a deal in which the two men would rotate the premiership. A late-night meeting on Tuesday between Mr. Gantz and Mr. Netanyahu ended abruptly and without results about an hour after it started.

As time ran out for Mr. Gantz and Mr. Netanyahu to reach a deal, the focus shifted to who was to blame.

Mr. Netanyahu, who remains prime minister of a caretaker government until a new one is formed, said he had exhorted Mr. Gantz to join forces in a unity coalition because urgent defense budget issues needed to be addressed and the security of Israel was at stake.

Mr. Gantz’s only other option for forming a government was doomed earlier Wednesday.

There had been speculation that he could form a narrow, minority government without Mr. Netanyahu and his right-wing and ultra-Orthodox allies. It would have entailed a few smaller parties joining him in the coalition or supporting it from the outside.

But a minority government would require the cooperation of legislators from the Joint List of predominantly Arab parties in the Parliament and of Avigdor Liberman’s ultranationalist Yisrael Beiteinu party. On Wednesday, Mr. Liberman ruled out any prospect of going along with that plan. At a news conference, he described the Arab politicians as an anti-Zionist “fifth column.”

A former coalition partner of Mr. Netanyahu’s, Mr. Liberman also rejected returning to a narrow government with Mr. Netanyahu and his ultra-Orthodox allies, describing them, too, as increasingly anti-Zionist.

The first election, in April, gave Mr. Netanyahu an advantage, but he failed to assemble a majority coalition prompting a second election.

In the September election, Mr. Gantz’s Blue and White party won 33 seats, edging ahead of Mr. Netanyahu’s Likud, which won 32. But Mr. Netanyahu secured the endorsements of 55 right-wing and religious members of Parliament for the premiership, one more than Mr. Gantz did.

Mr. Liberman, a former Netanyahu ally turned rival, held the balance with the eight seats won by his party and appeared to relish his role as potential kingmaker. He has issued both political pleas and ultimatums to try to get Mr. Gantz and Mr. Netanyahu to compromise and join forces, though Likud and Blue and White commanded enough seats between them to form a joint government without him.

As leader of the larger parliamentary bloc, Mr. Netanyahu was given the first chance to try to form a government. He abandoned the effort days before his six-week deadline ran out. Mr. Gantz was then given four weeks to try and succeed where the seasoned Mr. Netanyahu had failed.

Mr. Netanyahu’s insistence to go first as prime minister under any rotation agreement with Mr. Gantz has been a major sticking point in the negotiations for a unity coalition.

Taking the leadership role first in any coalition agreement is important to Mr. Netanyahu because as an ordinary minister he would have to resign immediately if indicted. Under current Israeli law, a prime minister charged with crimes may remain in office until a final court verdict, after the appeals process has been exhausted — a process that could take years.

That was a non-starter for most of the Blue and White leadership. The party had repeatedly pledged to its voters not to serve in a government under a prime minister facing a serious indictment.

In addition, Mr. Netanyahu insisted on bringing his entire right-wing, religious bloc of 55 members of Parliament into any coalition, over Blue and White’s vehement objections.

Israel’s president, Reuven Rivlin, whose role is largely ceremonial, had been pushing for a unity government and presented his own proposal to try to resolve the impasse. He suggested that Mr. Netanyahu go first as prime minister and, if indicted, declare himself incapacitated for an indefinite period.

Mr. Netanyahu embraced the idea, but Blue and White’s leaders had difficulty accepting it.

The talks for a unity government meant to heal national rifts took place in an atmosphere of unfettered divisiveness.

Mr. Netanyahu accused Mr. Gantz of having plotted all along to form a narrow government with the support of Arab members of Parliament, and described such a government as “dangerous for Israel.” Netanyahu critics denounced the prime minister’s rhetoric as racist, saying it incited violence.

For his part, Mr. Gantz condemned Mr. Netanyahu’s alliance with right-wing and ultra-Orthodox parties as an “immunity bloc,” meant to try to provide him with parliamentary protection from prosecution.

The political drama is not the only challenge facing Israel right now.

On Wednesday, the Israeli military said it had conducted strikes against dozens of Iranian military sites in Syria. The strikes came a day after rockets were fired out of Syria at the Israeli-controlled Golan Heights and were intercepted by Israel, causing no harm.