Benjamin Netanyahu, Israel’s longest-serving prime minister, has weathered many controversies, including accusations of corruption and allegations this year that a contentious overhaul of the country’s judiciary was a poorly disguised power grab.

But he now faces the greatest crisis of his political career. The backlash to his government’s failures to prevent the Oct. 7 Hamas-led terrorist attack, in which 1,200 people were killed and more than 240 others taken hostage, and criticism of his handling of the war in Gaza, are steadily growing.

People both inside Mr. Netanyahu’s government and those who hope to see him replaced agree that his standing has never been so low with the Israeli public.

And yet — owing to the complexities of Israel’s parliamentary system and the vagaries of war — few paths exist for Mr. Netanyahu to be ousted soon from office. His long-term political prospects and his legacy, however, rest largely on how he handles the coming days, analysts said.

In recent days and weeks, vigils for slain Israelis have turned into protests over Mr. Netanyahu’s leadership. Calls for him to take responsibility for the intelligence failures that preceded the Hamas attack have morphed into a campaign seeking his resignation.

A far-right member of his governing coalition, Itamar Ben-Gvir, has threatened to topple the government. Members of Mr. Netanyahu’s own Likud party have talked about defecting, according to two senior party members. And the United States, Israel’s closest and most important ally, has begun pushing the prime minister to limit the number of civilian deaths in Gaza.

As the war entered a new phase on Friday after the collapse of a seven-day truce and the start of a renewed Israeli air campaign, Mr. Netanyahu is searching for a solution — including the potential assassination of Hamas’s top leader in Gaza — that could appease his coalition, silence his critics and satisfy a population desperate for him to both bring home the remaining hostages from Gaza and defeat Hamas.

There is strong support for the war across the political spectrum, and one opposition party has joined Mr. Netanyahu’s coalition to form an emergency unity government and war cabinet. The move of unity was widely celebrated by the Israeli public as a sign that politicians were cutting through red tape to manage the war effort. But Mr. Netanyahu still must manage differences in the leadership over the hostage talks, humanitarian aid and the conduct of the war. Mr. Ben-Gvir, for example, had threatened during the cease-fire to bring down the government if the war did not resume.

In a statement to reporters on Friday, Mr. Netanyahu said that he was committed to “destroying Hamas.” Privately, he has told aides that he is pushing for the military to assassinate the head of Hamas in Gaza, Yahya Sinwar, according to a current Israeli official and a former one who have spoken with the prime minister in recent days.

Mr. Netanyahu believes, the officials said, that the assassination of Mr. Sinwar, the presumed mastermind of the Oct. 7 attacks, would be enough to convince the Israeli public that a major victory had been won against Hamas and the war can end.

Israeli political analysts said Mr. Sinwar’s death could stem, but not reverse, the tide of public anger directed at Mr. Netanyahu.

“If the Israeli military succeeded in assassinating a major Hamas figure, I expect Netanyahu would seek to take credit,” said Anshel Pfeffer, a columnist for Haaretz newspaper, and the author of “Bibi: The Turbulent Life and Times of Benjamin Netanyahu.”

Mr. Pfeffer added that despite the many past scandals that have rocked Mr. Netanyahu’s reputation, he has always managed to save his political skin.

For much of the past year, hundreds of thousands of Israelis have taken to the streets to protest the prime minister’s plans for a judicial overhaul. Many Israelis see the changes as tied to Mr. Netanyahu’s ongoing trial on charges of corruption, though he has denied any connection between the two.

In a Sept. 7 poll by Kan, Israel’s public broadcaster, 75 percent of respondents said that they believed that Mr. Netanyahu’s government was “not functioning well.”

But in the weeks since the start of the war, Mr. Netanyahu’s numbers have steadily dropped. In a poll released on Friday by the Israeli newspaper Ma’ariv, 30 percent of respondents said that Mr. Netanyahu was best fit to serve as prime minister, while 49 percent preferred his closest political rival, Benny Gantz, a former defense minister.

The same poll found that support for Likud had also fallen.

In Israel, governments are formed through a multiparty system based on which party can cobble together a majority of at least 61 seats in the 120-seat Parliament.

Mr. Netanyahu’s coalition currently holds 74 seats. To topple him, at least 13 members of Parliament would need to leave his coalition or a no-confidence vote would have to be held in the legislature with another candidate selected to replace Mr. Netanyahu.

Aviv Bushinsky, a former political adviser to Mr. Netanyahu, said that neither scenario was likely.

“Almost everyone you speak to today will tell you the same thing — that Netanyahu must step down from office — he cannot continue to lead this country,” said Mr. Bushinsky. “And yet, at the same time, there is a very real scenario in which he remains prime minister despite his unpopularity because of the difficulty in replacing or removing him.”

Mr. Bushinsky said that some members of Mr. Netanyahu’s Likud party had spoken about splintering to form their own party, but they were unlikely to do so in the midst of a war.

“People are only going to strike while the iron is hot,” Mr. Bushinsky said. “It’s not just about them leaving Likud; it is about them being able to put together their own coalition of 61 people who will support them. I just don’t see a political constellation like that which will work.”

Israeli political sentiment, he added, has shifted to the right since Oct. 7. Any future election, he predicted, could be won only by a right-wing candidate who was seen as a strong military leader.

Many of the Israelis who gathered on Friday afternoon in Tel Aviv’s so-called Hostage Square agreed with Mr. Bushinsky. The large area outside the Tel Aviv Art Museum has become a regular site of protest, mourning and celebration for the families of those abducted from Israel and taken to Gaza on Oct. 7.

On Thursday, Moran Gal, 24, and her boyfriend came to the square to cheer and celebrate the return of eight Israeli hostages. But by Friday, with the cease-fire ended and reports trickling out that some of the oldest hostages held by Hamas had been killed, Ms. Gal had tears on her face.

“This is all Bibi’s fault,” said Ms. Gal, a student, using Mr. Netanyahu’s nickname. “How come he hasn’t apologized? How come he hasn’t admitted he failed us?”

In Jerusalem, where almost-daily protests have been held in front of Parliament calling for Mr. Netanyahu’s resignation, hundreds gathered on Thursday night to listen to Eran Litman, whose daughter was killed on Oct. 7.

Mr. Litman accused the Israeli prime minister of failing to protect his daughter and of returning to war in Gaza instead of saving the lives of additional Israeli hostages.

“He only thinks about himself, not about his country,” said Mr. Litman.

“Shame,” a crowd of hundreds thundered each time he mentioned Mr. Netanyahu’s name.

Johnatan Reiss contributed research.