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Even more significant would be the death of Mohammed Deif, the shadowy figure who has survived several previous Israeli assassination attempts with severe injuries and was the target of Tuesday night’s attack. Mr. Deif’s fate remained unknown Thursday, though the body of his 3-year-old daughter, Sara, was recovered from the rubble of the Gaza City home where five one-ton bombs also killed Mr. Deif’s wife, baby son and at least three others.

Amos Yadlin, a former Israeli chief of military intelligence, called the killing of Mr. Deif’s three deputies “a very important operational achievement” and said that if Mr. Deif also turns up dead, “this will badly hurt Hamas’s military wing.”

“We’re now going to a war of attrition that was a threat of Hamas. Israel basically turned it upside down and said, ‘You want attrition? You are welcome. You lost your strategic military tools against Israel. Our firepower and our intelligence and our capability to sustain more days is much bigger than yours.’ This is the strategy.

The Gaza Health Ministry said Israeli airstrikes had killed at least 60 people since the collapse on Tuesday of cease-fire negotiations in Cairo and the resumption of violence after nearly nine days of quiet, bringing the Palestinian death toll in the operation that began July 8 close to 2,100.

As the conflict grinds on, Israelis see time as on their side. Experts estimate that Hamas began the summer with a stockpile of about 10,000 rockets. It has fired nearly 4,000, according to the Israeli military, which says it has taken out at least 3,000 more. So it cannot keep launching at this pace for long.

With Israel and the Palestinians apparently still far apart on terms for a durable truce, analysts suggested settling in for days or even weeks more of cross-border air exchanges, after what is already the longest Israeli military operation in decades. Diplomatic pressure appeared to be easing, if only because the world’s attention seems focused on other crises including the rise of Islamic extremists in Iraq and Syria, the Ebola outbreak in Africa and civil unrest in Ferguson, Mo.

Israel has much vaster resources, though its politicians and people are increasingly fractured over the prosecution of the campaign. There are growing calls for a more aggressive ground invasion, which Prime Minister Benjamin Netanyahu has resisted, and intense opposition to the idea of making concessions in a cease-fire agreement that might seem to reward Hamas.

In Gaza, time is a liability. The number of displaced residents seeking shelter in United Nations schools swelled to nearly 300,000 as the violence resumed; officials have already given up any hope of classes starting Sunday as planned.

When Sergeant Shalit was exchanged for 1,000 Palestinian prisoners in October 2011 after Hamas held him in captivity for five years, it was Mr. Attar seen in a video ushering him from a pickup truck. Mr. Abu Shamalah, the Israeli military said, was also involved in a 2004 tunnel attack that killed six soldiers, and the 1994 murder of an Israeli officer in Rafah.

“Israel can play that game for a long time, certainly longer than Hamas can. That’s true on a purely military level, but the fact is, as the war drags on, it’s going to be harder and harder for Netanyahu not to do one of those two things.”

In the Rafah refugee camp, a friend of Mr. Abu Shamalah’s said he had last seen him at the onset of the war, with Mr. Attar, and that he had said then he hoped to be a martyr.

Others move deep into the West Bank to claim land for Jews, out of religious fervor and/or a desire to see more or all of the West Bank absorbed into Israel. While Israel officially forbids this and often evicts these settlers, many are still able to take root.

The simple version is that violence has become the status quo and that trying for peace is risky, so leaders on both ends seem to believe that managing the violence is preferable, while the Israeli and Palestinian publics show less and less interest in pressuring their leaders to take risks for peace.

That sense of Palestinian hopelessness and distrust in Israel and the peace process has been a major contributor to violence in recent years.

"We don't have a partner for peace."

9 questions about the Israel-Palestine conflict you were too embarrassed to ask

Militants in Gaza have since stepped up rocket attacks against Israel, and Israeli airstrikes on the enclave intensified.

He voiced support for international efforts, led by Egypt, for a sustainable ceasefire, and expressed hope that today’s humanitarian pause can lead to a “more durable calm.”

Jews themselves are launching missiles at their own people

Do you have another suggestion for how to deal with terrorists in short term?