Israeli troops have begun pulling out of Gaza after Hamas and other Palestinian factions announced they will give Israel a one-week cease-fire starting Sunday.

The move comes as Israeli Prime Minister Ehud Olmert says he wants to withdraw Israel's forces from the Gaza Strip as soon as possible.

Olmert said Sunday that Israel has no intention of remaining in Gaza, but wants assurances that a new cease-fire with the Hamas militant group will be stable.

Hamas announced a one-week cease-fire on Sunday, a day after Israel said it was ending a three-week offensive in Gaza.

Olmert spoke at a dinner he hosted with visiting European leaders. The leaders came from a summit in Egypt where they discussed ways to ensure the cease-fire lasts.

An Islamic Jihad official in Gaza confirmed in a phone call to FOX News that Hamas and all the Palestinian factions have agreed on a cease-fire. Hamas is giving Israel one week to pull out the troops out of Gaza.

A senior Hamas official also said the group's wing in Syria agreed to a weeklong cease-fire.

Hamas' Syrian-based deputy leader, speaking for the militant Palestinian factions, said on Syrian television that the cease-fire will give Israel time to withdraw and open all the border crossings to allow humanitarian aid into Gaza.

The Islamic Jihad's Daoud Shihab told The Associated Press that the factions will jointly make a formal announcement later on Sunday.

Shihab says a longer cease-fire will be conditional on Israel withdrawing from Gaza the troops it sent into the strip two weeks ago. He says the militants will also demand that Israel open border crossings into Gaza.

News of the cease-fire came after militants in Hamas-ruled Gaza fired salvoes of rockets into southern Israel on Sunday, defying a unilateral cease-fire called by Israel and threatening to reignite three weeks of violence that Palestinian medics say has killed more than 1,000 people and turned Gaza's streets into battlegrounds.

An Israeli security chief told Cabinet ministers the military operation "is not over" and that the next few days would be critical to determining whether it would be relaunched.

The military said no one was injured by more than a dozen rockets that struck southern Israel even as a slew of foreign leaders traveled to Egypt to try to cement the newly declared cease-fire. Later, security officials in the northern Gaza town of Beit Hanoun reported an Israeli airstrike wounded a woman and her child.

After the first volley hit the rocket-scarred town of Sderot, Israeli aircraft hit the rocket squad that fired it, the military said.

In another incident after the truce took hold, militants fired small arms at an infantry patrol, which directed artillery and aircraft to strike back, the military said.

"Israel's 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," Israeli Prime Minister Ehud 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."

Click here for photos of the conflict.

Government spokesman Mark Regev would not say what level of violence would provoke Israel to call off the cease-fire.

In Gaza, people loaded vans and donkey carts with mattresses and began venturing back to their homes to see what was left standing after the punishing air and ground assault the tiny seaside territory endured. Bulldozers began shoving aside rubble in Gaza City, the territory's biggest population center, to clear a path for cars while medical workers sifting through mounds of concrete said they discovered 75 bodies. discovered dozens of bodies in the debris.

The cease-fire went into effect at 2 a.m. Sunday local time after three weeks of fighting that killed some 1,200 Palestinians, about half of them civilians, according to Palestinian and United Nations officials. At least 13 Israelis also died, according to the government.

An official who attended the Israeli Cabinet meeting quoted internal security service chief 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," security chief Yuval Diskin was quoted as saying. The official spoke on condition of anonymity because Cabinet meetings are closed.

Israel stopped its offensive before reaching a long-term solution to the problem of arms smuggling into Gaza, one of the war's declared aims. And Israel's insistence on keeping soldiers in Gaza raised the prospect of a stalemate with the territory's rulers.

The cease-fire went into effect just days ahead of President-elect Barack Obama's inauguration Tuesday. Outgoing Secretary of State Condoleezza Rice said the Bush administration welcomed Israel's decision and a summit set for later Sunday in Egypt is meant to give international backing to the truce.

Leaders of Germany, France, Spain, Britain, Italy, Turkey and the Czech Republic — which holds the rotating European Union presidency — are expected to attend along with Palestinian President Mahmoud Abbas, Egyptian President Hosni Mubarak and U.N. chief Ban Ki-moon.

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, declaring that "the United Nations is ready to act."

Israel said it was not sending a representative to the meeting. Hamas, shunned internationally as a terrorist organization, was not invited. However, the group has been mediating with Egypt and any arrangement to open Gaza's blockaded borders for trade would likely need Hamas' acquiescence.

In announcing the truce late Saturday, Prime Minister Ehud Olmert said Israel would withhold fire after achieving its goals and more.

"Hamas was hit hard, in its military arms and in its government institutions. Its leaders are in hiding and many of its men have been killed," Olmert said.

If Hamas holds its fire, the military "will weigh pulling out of Gaza at a time that befits us," Olmert said. If not, Israel "will continue to act to defend our residents."

In Gaza, people began to take stock of the devastation. The Shahadeh family loaded mattresses into the trunk of a car in Gaza City, preparing to return to their home in 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 the southern town of Rafah, where Israel bombed dozens of smuggling tunnels, construction worker Abdel Ibn-Taha said he was very happy about the truce. "We're tired out," he said.

Schools in southern Israel remained closed in anticipation of possible rocket fire. Shortly before the rocket volley Sunday, the head of the Parents Association in the border town of Sderot, Batya Katar, said she was disappointed with the unilateral nature of the truce and the fact that Israel did not reach an agreement directly with Hamas, which Israel shuns.

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

Israel apparently reasons that the two-phase truce would give it ammunition against its international critics: Should Hamas continue to attack, then Israel would be able to resume its offensive after having tried to end it. It was not immediately clear how many rockets would have to fall to provoke an Israeli military response.

Hamas, which rejects Israel's existence, violently seized control of Gaza in June 2007, provoking a harsh Israeli blockade that has deepened the destitution in the territory of 1.4 million Palestinians. The Israeli war did not loosen Hamas' grip on Gaza, and the group vowed that a unilateral cease-fire was not enough to end the Islamic movement's resistance.

"The occupier must halt his fire immediately and withdraw from our land and lift his blockade and open all crossings and we will not accept any one Zionist soldier on our land, regardless of the price that it costs," Hamas spokesman Fawzi Barhoum said.

More moderate Palestinians also reacted with skepticism to Israel's two-phase truce and called on world leaders attending the Egypt summit to press Israel to pull out its troops immediately.

"This 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.

The Associated Press contributed to this report.