As the Biden administration and its allies try to secure an elusive cease-fire in Gaza, Israel appears to have gone rogue.

Benjamin Netanyahu, Israel’s prime minister, came to Washington last week to give a defiant speech. Despite international condemnation, he vowed to continue the war against Hamas in Gaza and the West Bank, where Israel is killing and imprisoning scores of Palestinians each week, without any clear idea of its endgame.

The assassinations of senior Hezbollah and Hamas figures abroad have now sharply raised the risks of a larger regional war as Iran, Hamas and Hezbollah prepare retaliation, analysts say.

But the deaths of Fuad Shukr, a senior Hezbollah commander, and Ismail Haniyeh, the political leader of Hamas, will not change the strategic quandary Israel faces over how to end the war, govern Gaza or care for the civilians there. They are more likely to intensify the conflict than diminish it, making progress on a Gaza cease-fire even more difficult.

Israel says it does not want to occupy Gaza, but has no other solution to provide order; Hamas refuses to surrender, despite the thousands of dead. While Washington sees a cease-fire followed by a regional deal as an answer, Mr. Netanyahu is contemptuous of the idea. He believes only force will compel Hamas to concede and restore Israel’s strategic deterrence toward Iran and its proxies, especially Hezbollah.

Absent a clear goal in the war, however, Mr. Netanyahu’s defiance is dividing Israel from its allies and the country itself. It has further shaken trust in his leadership. It is fueling suspicions that he is keeping the country at war to keep himself in power. It is intensifying a deep rift inside the society — about the fate of Israeli hostages, the conduct of the war and the rule of law — that is challenging the institutional bonds that hold Israel together.