Tens of thousands of panicked residents fled their homes in the northern Gaza Strip on Sunday after the Israeli military dropped leaflets from the sky warning those who stayed behind that they were risking their lives because a large, intense operation was imminent.

Residents in Gaza were whipsawed by growing anxiety and frustration. More than 17,000 people poured into makeshift shelters as Israeli commandos entered the coastal enclave early Sunday to target a Hamas rocket-launch site. A gun battle with Hamas militants ensued and left four Israeli soldiers lightly wounded, an army spokesman said.

The brief incursion by commandos followed the single deadliest Israeli bombing of the six-day campaign.

Israeli missiles hit a house where Gaza’s police chief, Tayseer al-Batsh, was praying Saturday night. The explosions killed 18 members of his extended family, including six children, and sent the top Hamas law-enforcement officer into intensive care, where he was clinging to life Sunday.

On Monday, Israel said it shot down a drone that was flying over the southern Israeli city of Ashdod. This appeared to mark the first deployment of unmanned aircraft by Hamas from Gaza.

The drone was intercepted by a U.S.-supplied Patriot air-defense missile. An Israeli military spokesman said crews were looking for the debris.

The weekend violence in Gaza came as Israeli Prime Minister Benjamin Netanyahu indicated that Israel has no interest in halting its assault. Israel’s objective, he said at his weekly cabinet meeting, is to inflict “a significant blow on Hamas” that will yield “the restoration of quiet for a long period.”

That goal closely tracks Israel’s ambition in two previous offensives against Hamas — in the winter of 2008-2009 and in late 2012 — both of which succeeded in setting back the Islamist movement’s capabilities, but not for very long. In each case, Israel won just a few years of relative calm, even as Hamas’s rocket range and weapons arsenal expanded.

The cycle has come to be known in Israel as “mowing the lawn” — a temporary disruption of Hamas’s ability and will to fire rockets.

Pressure is growing in Israel to make sure that this time is different.

“The army should not stop until they wipe out Hamas,” said Avner Peretz, 46, just minutes after the windows in his brother-in-law’s house were blown out by a Hamas rocket attack in the southern Israeli town of Netivot over the weekend. “The last two conflicts, we came out looking like the losers. This time, we need to be the winner.”

So far, there’s no doubt that Israel has inflicted far more damage than Hamas, but that’s consistently true in this deeply asymmetrical fight.

There have been 169 residents of Gaza killed in the current Israeli operation, including 36 children and 24 women, according to the Gazan Health Ministry. The United Nations estimates that three-quarters of the dead are civilians.

Hamas and its allies have fired hundreds of rockets into Israel — including 130 on Sunday — but most have either landed in open areas or been shot down by Israel’s sophisticated anti-missile system, Iron Dome. Several Israelis have been seriously injured by the rocket fire, but none have been killed.

Israel Radio reported late Sunday that two rockets were fired at Israel from Syria, apparently from Syrian army positions. Israel responded with artillery fire.

A more isolated Hamas

The U.N. Relief and Works Agency on Sunday called the situation in Gaza “devastating and unpredictable.”

In central Gaza, where Israeli missiles hit the house where the police chief was staying Saturday, there are 17 fresh graves, the bodies marked by mounds of earth, with cinderblock for headstones.

The police chief may not have been widely liked in Gaza — his police are aggressive and zealous in their defense of Hamas — but he was respected. The incidence of ordinary crime in Gaza is low.

One of his nephews, Ahmed al-Batsh, 26, lay in a hospital bed in Gaza, his head swaddled in bandages and his neck and back peppered with shrapnel. “More will die,” he said.

He blamed the United States for supplying Israel with $3 billion a year in military aid. “These bombs are bought by America,” he said, staring through one good eye.

Israeli officials and analysts say there’s little chance that Israel will try to destroy Hamas entirely, given the enormous cost and risk involved. But they say Israel has several key advantages it lacked the last two times it traded blows with Hamas.

Hamas is far more isolated internationally. The Gaza leaders have alienated their former patron in Damascus, Syrian President Bashar al-Assad, by siding with that country’s rebels.

And Hamas lost its closest ally last year when Mohamed Morsi, the Islamist president of Egypt, was ousted and replaced by a military-backed government that sees Hamas much the same way Israel does: as an enemy.

“Egypt is doing just about everything it can to make sure Hamas gets hurt by the Israelis,” said Itamar Yaar, a former top official with Israel’s national security council. “They’ll be happy if Hamas disappears.”

Egyptian authorities once looked the other way as Hamas used tunnels beneath the Gaza border to load up on rockets. But Egypt has essentially shut down all tunnel traffic.

Hamas’s long-range rockets could be especially tough to replace. The group can produce its own shorter-range weapons for hitting southern Israel, but it has smuggled — through the border tunnels — rockets from its backers in Iran that are able to target Tel Aviv, Jerusalem and other major population centers in Israel’s central core, Israeli officials say.

A senior Israeli air force official said Sunday that Hamas began the current conflict with “hundreds” of longer-range rockets and that the air force has made it a priority to destroy as many as possible.

But the official acknowledged that eliminating the arsenal is impossible.

“You can’t stop the rockets,” said the official, who spoke on the condition of anonymity to freely discuss Israel’s strategy and tactics. “You can only make them decide to stop shooting. They have thousands of rockets, and you can’t attack all of them.”

Hamas’s battered finances may be adding to Israel’s leverage. Hamas has been unable to pay government workers for months. Yaar said Hamas may be willing to promise a period of calm in exchange for Israeli cooperation in reviving the devastated Gazan economy.

But such a deal would require cease-fire talks.

Michael Herzog, a former top Israeli military official who has conducted past negotiations, said Sunday that Hamas wants a reopening of the border crossing with Egypt, the release of prisoners and money to pay Gaza’s 40,000 government employees.

Israel, meanwhile, wants a guarantee of several years of peace, at least, without appearing to reward Hamas’s militant behavior.

“It’s challenging to bring this conflict to a conclusion, because the two parties have totally different pictures of how they want it to end,” Herzog said.

In Gaza, ordinary citizens were just hoping for a night’s rest. Many of those who abandoned their homes in the north walked to Gaza City, with children waving white flags and mothers carrying mattresses. Farmers brought their donkeys.

“We came with nothing,” said Abdul Karim al-Attar, a farmer who arrived with his brothers, their wives and children, 38 in all.

Witte reported from Tel Aviv. Ruth Eglash in Jerusalem and Islam Abdel Karim in Gaza contributed to this report.