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JERUSALEM – The Israeli army says it has begun withdrawing its troops from Gaza after ending a three-week offensive in the territory.

The move comes shortly after Gaza's Hamas rulers announced a one-week cease-fire.

The Israeli military would not say how many troops it is pulling out. But tanks were rolling out early Sunday and smiling infantry soldiers were seen walking toward the border.

Israel announced a unilateral cease-fire late Saturday. It says it will keep at least some troops in Gaza while arrangements are made to prevent Hamas from rearming.

THIS IS A BREAKING NEWS UPDATE. Check back soon for further information. AP's earlier story is below.

GAZA CITY, Gaza Strip (AP) — Hamas offered Israel an immediate weeklong truce Sunday, hours after Israel silenced its guns and grounded its aircraft, but the Islamic militant group conditioned long-term quiet on a complete Israeli withdrawal from the territory.

Militant rockets peppered southern Israel ahead of the Palestinian truce offer, threatening to re-ignite three weeks of violence that killed more than 1,200 Palestinians — more than half of them civilians, Gaza officials said — and turned the streets of Hamas-ruled Gaza into battlegrounds.

In Gaza, Palestinians loaded vans and donkey carts with mattresses and ventured out to see what was left of their homes after Israel's punishing air and ground assault. Bulldozers shoved aside rubble in Gaza City to clear a path for cars. Medical workers sifting through mounds of concrete said they recovered 100 bodies amid the debris.

Israel mounted the offensive three weeks ago to halt years of rocket attacks, but despite the latest barrage, the government spokesman said Israel's cease-fire offer stood. Thirteen Israelis died during the offensive, including four killed by rocket fire.

"We will honor our cease-fire as we said last night and will only act to defend ourselves if we see Hamas provocation," the spokesman, Mark Regev, said in response to the Hamas cease-fire announcement.

But Israel said its troops in Gaza would not leave until rocket fire halted entirely.

The Palestinian cease-fire offer was announced by military leaders in Gaza and in Damascus, Syria, the base of Gaza's exiled Hamas leaders. They did not set a time, but it appeared to be effective immediately.

In Damascus, Moussa Abu Marzouk, Hamas' deputy leader, told Syrian TV that the cease-fire would last a week to give Israel time to withdraw and open all Gaza border crossings to let humanitarian aid into the embattled seaside territory.

"We the Palestinian resistance factions declare a cease-fire from our side in Gaza and we confirm our stance that the enemy's troops must withdraw from Gaza within a week," Abu Marzouk said.

Hamas, which rejects Israel's right to exist, violently seized control of Gaza in June 2007, provoking a harsh Israeli blockade that has deepened the destitution in the territory and confined 1.4 million Palestinians to the tiny coastal strip. Egypt has also kept its border with Gaza largely sealed.

Militants did not back down from their demand that Israel ultimately open blockaded crossings, which serve as economic lifelines for Gaza.

The Hamas offer raised hopes that the cease-fire would stick more than a few hours. Militants had fired 17 rockets into Israel on Sunday, slightly injuring three people, police said, even as foreign leaders tried cement an end to the war in Egypt. Israel briefly retaliated against the rocket assaults with air and artillery strikes.

In Gaza City, the Shahadeh family was loading mattresses into the trunk of a car in Gaza City, preparing to return home to the hard-hit northern Gaza town of Beit Lahiya.

"I've been told that the devils have left," said Riyadh Shahadeh, referring to the Israelis. "I'm going back to see how I'm going to start again. I don't know what happened to my house. ... I am going back there with a heart full of fear because I am not sure if the area is secure or not, but I have no other option."

In southern Israel, residents who have endured rocket attacks for eight years accused the government of stopping the offensive too soon. Israel declared the cease-fire before reaching a long-term solution to the problem of arms smuggling into Gaza, one of the war's declared aims.

Schools in southern Israel had remained closed in anticipation of the rocket fire that was swift to come. Shortly before the rocket fire resumed, the head of a parents association in the town of Sderot faulted the government for not reaching an agreement directly with Hamas, which Israel shuns.

"It's an offensive that ended without achieving its aims," Batya Katar said. "All the weapons went through Egypt. What's happened there?"

"The weapons will continue to come in through the tunnels and by sea," she said.

Before Hamas made its cease-fire offer, Israeli Prime Minister Ehud Olmert warned militants not to attack.

"Israel's (cease-fire) decision allows it to respond and renew fire at our enemies, the different terror organizations in the Gaza Strip, as long as they continue attacking," Olmert said at the start of the weekly Cabinet session.

"This morning some of them continued their fire, provoking what we had warned of," Olmert said. "This cease-fire is fragile and we must examine it minute by minute, hour by hour."

Cabinet Secretary Oved Yehezkel quoted the head of the Shin Bet security service, Yuval Diskin, as telling ministers that "the operation is not over."

"The next few days will make clear if we are heading toward a cease-fire or the renewal of fighting," Diskin was quoted as saying.

The Israeli operation outraged the Muslim world, sparking dozens of demonstrations. On Sunday, Qatar announced that it had closed Israel's trade office in the small Gulf Arab state and ordered its staff to leave within seven days.

Qatar is the only Gulf Arab state that has ties with Israel.

Leaders of Germany, France, Spain, Britain, Italy, Turkey and the Czech Republic — which holds the rotating European Union presidency — headed for Egypt to lend international backing to the cease-fire. Palestinian President Mahmoud Abbas, Egyptian President Hosni Mubarak and U.N. chief Ban Ki-moon were also expected to attend.

Ban welcomed the Israeli move and called on Hamas to stop its rocket fire. "Urgent humanitarian access for the people of Gaza is the immediate priority," he said.

Israel said it was not sending a representative to the meeting. But Sunday evening, leaders from Britain, Germany, Spain, Italy and France and the European Union were coming to Jerusalem for a working dinner with Olmert.

Hamas, shunned internationally as a terrorist organization, was not invited to the summit in Egypt. But the group has been mediating with Egypt, and any arrangement to open Gaza's blockaded borders for trade would likely need Hamas' acquiescence.

Abbas, too, echoed Hamas' call for a total Israeli withdrawal and the lifting of bruising Israeli sanctions.

Israel's cease-fire "is an important and necessary event but it's insufficient," said Abbas, Hamas' bitter rival and the top leader in the West Bank, the larger of the two Palestinian territories. "There should be a comprehensive Israeli withdrawal from Gaza, a lifting of the siege and a reopening of crossings" to aid, he said, speaking from Egypt.

Under the truce plan, Hamas would not rearm, as militants did during a 6-month truce that preceded the war. In a step toward achieving those guarantees, Israel on Friday won a U.S. commitment to help crack down on weapons smuggling into Egypt and from there, to Gaza.

But Egyptian Foreign Minister Ahmed Aboul Gheit said Saturday that his country would not be bound by the agreement. Egypt's cooperation is essential if the smuggling is to be stopped.

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