GAZA CITY, Gaza Strip — Palestinian militants fired hundreds of rockets from the Gaza Strip into Israel on Wednesday, while Israel pressed ahead with a series of airstrikes that have killed 21 Palestinians, including three senior militants and at least 10 civilians.

Egypt Attempts to Broker Cease-Fire

A state-run Egyptian TV station announced that Egypt, a frequent mediator between the sides, had brokered a cease-fire. But the truce efforts appeared to falter as fighting intensified late Wednesday, with neither side showing any sign of backing down.

In a prime-time TV address, Israeli Prime Minister Benjamin Netanyahu claimed that Israel had dealt a harsh blow to the militants. But he cautioned: “This round is not over.”

“We say to the terrorists and those who send them. We see you everywhere. You can’t hide, and we choose the place and time to strike you,” he said, adding that Israel would also decide when calm is restored.

Throughout the day, rocket fire set off air-raid sirens throughout southern and central Israel, some 80 kilometers (50 miles) away. Residents had been bracing for an attack since Israel launched its first airstrikes early Tuesday.

Signs of Restraint from Both Sides

It was the heaviest fighting between the sides in months, pushing the region closer toward a full-blown war. But in signs that both sides were trying to show restraint, Israel avoided attacks on the ruling Hamas militant group, targeting only the smaller and more militant Islamic Jihad faction. Hamas, meanwhile, appeared to remain on the sidelines.

Israel and Hamas have fought four wars since the Islamic militant group took control of Gaza in 2007.

Late Wednesday, Egypt’s Extra News television channel, which has close ties to Egyptian security agencies, said it had brokered a cease-fire. Egyptian intelligence frequently mediates between Israel and Palestinian militants.

Israeli officials confirmed that Egypt was trying to facilitate a cease-fire. Speaking on condition of anonymity to discuss behind-the-scenes diplomacy, they said Israel would evaluate the situation based on actions on the ground, not declarations.

Islamic Jihad Continues Rocket Fire

Islamic Jihad said it would continue firing rockets. Mohamad al-Hindi, an official with the group, said a sticking point in the talks was that the Palestinians wanted an Israeli commitment to stop targeted killing operations, such as the ones that killed three top Islamic Jihad commanders early Tuesday.

As rockets streaked through the sky, Israeli TV stations showed air defense systems intercepting rockets above the skies of Tel Aviv. In the nearby suburb of Ramat Gan, people lay face-down on the ground as they took cover.

The Israeli military said that for the first time, an air-defense system known as David’s Sling intercepted a rocket. The system, developed with the U.S., is meant to intercept medium-range threats and is part of a multi-layered air defense that also includes the better-known Iron Dome anti-rocket system. Israeli media said a previous attempt to use the system several years ago had failed.

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Jewish Ultranationalist Parade Raises Tensions

In a move that could further raise tensions, Israeli police said they would permit a Jewish ultranationalist parade to take place next week. The parade, meant to celebrate Israel’s capture of east Jerusalem and its Jewish holy sites, marches through the heart of the Old City’s Muslim Quarter and often leads to friction with local Palestinians.

Israeli officials said over 400 rockets had been fired as of Wednesday evening. Most, they said, were intercepted or fell in open areas, but Defense Minister Yoav Gallant said about one-quarter had been misfired and fallen inside Gaza. Israeli rescuers said three people were hurt running for shelter, and four homes in southern Israel were damaged by rocket strikes.

The army said that schools would remain closed and restrictions on large gatherings would remain in place in southern Israel until at least Friday. Residents were instructed to stay near bomb shelters.

Eden Avramov, a 26-year-old resident of the southern Israeli town of Sderot, described the 24 hours since Israel launched airstrikes on Gaza as terrifying. “We are all traumatized from this routine — the waiting, the booms, the alarms.”

Israeli aircraft hit targets in Gaza for the second straight day, killing at least five Palestinians. The Israeli military said its warplanes targeted dozens of rocket launchers, arms warehouses and other targets across the enclave. The Popular Front for the Liberation of Palestine said four of the dead were militants.

A 10-year-old Palestinian girl named Layan Mdoukh was killed in a blast at her home in Gaza City in unclear circumstances on Wednesday.

The initial Israeli airstrikes on Tuesday that set off the exchange of fire killed three senior Islamic Jihad militants and at least 10 civilians — most of them women and children. The Israeli military has said its attacks were focused on Islamic Jihad militant infrastructure in the coastal enclave.

Israel says the airstrikes are a response to a barrage of rocket fire launched last week by Islamic Jihad in response to the death of one of its members from a hunger strike while in Israeli custody.

Israel Aims to Avoid Conflict with Hamas

Israel says it is trying to avoid conflict with Hamas, the more powerful militant group that rules Gaza, and limit the fighting to Islamic Jihad.

“Our actions are meant to prevent further escalation,” said Rear Adm. Daniel Hagari, the Israeli military’s chief spokesman. “Israel is not interested in war.”

In a statement, an umbrella organization of Palestinian factions in Gaza, including Hamas, said the campaign against Israel — which it dubbed “Avenging the Free” — involved firing hundreds of rockets in retaliation for Israel’s killing of the three Islamic Jihad commanders as well as several civilians.

“The resistance is ready for all options,” the factions said. “If (Israel) persists in its aggression and arrogance, dark days await it.”

Still, it remained unclear whether Hamas had joined the fray. If the ruling militant group enters the fighting, the risk of a full-blown conflict would increase.

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High Civilian Toll Draws International Criticism

Israel has come under international criticism for the high civilian toll Tuesday, which included wives of two of the militant commanders, some of their children and a dentist who lived in one of the targeted buildings along with his wife and son.

In past conflicts, rights groups have accused Israel of committing war crimes due to high civilian deaths. Israel says it does its utmost to avoid civilian casualties and holds militant groups responsible because they operate in heavily populated residential areas.

In the Israeli-occupied West Bank, the military said that Palestinian gunmen opened fire at troops in the Palestinian town of Qabatiya in the northern West Bank during an army raid. Troops returned fire, killing the two men, and confiscated their firearms, it said.

Islamic Jihad later claimed the two men as its members.

Israel has been conducting near-daily military raids in the occupied West Bank for over a year to detain suspected Palestinian militants, including many from Islamic Jihad.

At least 107 Palestinians, around half of them militants, have been killed by Israeli fire in the West Bank and east Jerusalem this year, according to an Associated Press tally. At least 20 people have been killed in Palestinian attacks targeting Israelis.

Israel captured the West Bank, east Jerusalem and the Gaza Strip in the 1967 Mideast war. The Palestinians seek all three territories for a future independent state.