After a six-hour meeting, Israeli Prime Minister Benjamin Netanyahu and his security cabinet did not confirm the agreement, saying only that the Israeli military had been “instructed to continue its operations as necessary,” but Israeli news outlets reported that a cease-fire had been agreed to.

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Israeli officials’ reluctance to acknowledge a cease-fire underscores the delicate balancing act they are facing as they try to reach a long-term agreement with Hamas, which they view as a terrorist group bent on Israel’s destruction.

Before the latest flare-up, the two sides had been close to such a deal. It would have entailed economic aid for Gaza, including a cash injection and international reconstruction projects, in return for Hamas clamping down on border demonstrations and preventing the use of incendiary kites that have been launched across the border fence into Israel.

Analysts say that the two sides are not interested in another round of conflict but that both are grappling with internal pressure to show strength. Netanyahu, who is nearing an election year, has been criticized for his approach by right-wing members of his coalition and Israeli residents near Gaza. Hamas has been castigated by other militant factions in Gaza for dealing with the enemy.

“Even if they manage to get this cease-fire understanding going, we’ve seen how fragile they can be and I don’t expect it to last long,” said Ofer Zalzberg, an analyst with the International Crisis Group.

The violence on Monday and Tuesday was triggered by a botched Israeli operation inside Gaza on Sunday during which seven Palestinian militants were killed, including a Hamas commander. An Israeli officer was also killed.

The Israeli military said that about 460 rockets were launched from Gaza toward Israel. More than 100 were intercepted by Israel’s aerial defense system, but others struck residential buildings.

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Israeli jets responded with more than 160 airstrikes, which officials said targeted Hamas and Islamic Jihad, Gaza’s second-

largest militant faction. The attacks destroyed the headquarters of the Hamas-run al-Aqsa television station, other buildings housing its old offices and Hamas’s military intelligence bureau. The Israeli military said its naval forces also struck Hamas ships, as well as numerous weapons storehouses and manufacturing facilities.

In central Gaza City, near the seafront, the militant group’s four-story internal security building was reduced to rubble, which filled the street. Some houses were damaged as well.

“We were terrified. All the children in the house were screaming. The terror was in the eyes of everyone around us,” said Hafez Haboush, 29, who lives next to the internal security building. “After seeing these scenes and fear in the eyes of the children, I became aware that I do not want to have children so I do not suffer from losing them in Gaza.”

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Hossam al-Shami, 37, said he and his family fled their rented apartment near the television building when the airstrikes came close. Their home was badly damaged.

“I hope this tragedy does not recur. I’m looking for a new home to live in,” he said, adding, “There is no safe place.”

After cutting short an overseas trip and returning to Israel, Netanyahu remained conspicuously silent. Residents of Israel’s southern cities, forced to stay indoors and near protected areas, expressed anger that a long-term diplomatic solution to the continual rounds of hostilities has not been found.

Hundreds of residents of the southern Israeli city of Sderot protested Tuesday night against the cease-fire and Netanyahu.

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“I think it’s time the army went in and cleaned them out, cleaned the whole place,” said Shabtai Biran, a resident of Ashkelon, a coastal city a few miles from the northern tip of the Gaza Strip. “There are innocents here who are getting hurt.”

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One resident of his neighborhood, Shimshon, was killed and two women were seriously injured when a rocket hit their three-story apartment block. The man was a Palestinian from Hebron, in the West Bank.

Throughout the day, a steady stream of Israeli politicians arrived in the area. Some were more welcome than others. Tzipi Livni, an opposition leader and former peace negotiator, was chased away by angry residents in Shimshon. Tamar Zandberg, head of the left-wing Meretz party, also received a frosty reception. She said the situation was untenable for Israel and residents in the south in particular.

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“The problem is that the prime minister is always going for short-term solutions. While I support short-term solutions, they need to be part of a longer process,” Zandberg said. “I think that as soon as there is a cease-fire, everything needs to be done to reach a wider peace process.”

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Some members of Netanyahu’s coalition are pushing for more decisive action. Israeli Education Minister Naftali Bennett, leader of the right-wing Jewish Home party, has criticized attempts to broker a deal with Hamas. On Tuesday, after Israeli news reports that Bennett had supported a cease-fire, his office issued a statement describing them as “completely false.”

“At the cabinet, Minister Bennett presented his firm position as expressed in recent months and his plan to face the threat from Gaza,” his office said.

But Kobi Michael, an analyst at the Institute for National Security Studies, said the Israeli public, security establishment and politicians are for the most part behind efforts to reach a truce with Hamas.

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“Israel has no option,” he said. He noted that the Palestinian Authority, which governs the occupied West Bank, is unlikely to resume control in Gaza. “The consequence is the recognition of Hamas as the power in control of the Gaza Strip,” he said.

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Michael said the main threat to reaching a truce comes from Islamic Jihad, which has positioned itself to benefit from Hamas’s weakness amid growing unhappiness among Gaza’s 2 million residents. Gaza’s residents have faced severe trade and travel restrictions by Israel for more than a decade, and the border with Egypt is opened only sporadically.

Since early this year, Hamas had diverted some of the internal discontent toward Israel by encouraging weekly demonstrations along the border fence. Israeli officials say Hamas has used the border protests as a cover to carry out attacks and infiltrate Israeli territory.

In Gaza, some took to the streets Tuesday to celebrate after the cease-fire was announced. A rally was held near the television building to mark the “victory” against Israel.

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But past cease-fire deals have been short-lived, and in Israeli cities such as Ashkelon, frustrations are running high.

“It is not right that we are sitting here scared. It is them that should be scared,” said Biran, the resident of Ashkelon, referring to Hamas.