A Palestinian boy writes on a shrapnel-riddled backboard at the heavily damaged Sobhi Abu Karsh school in Gaza. (Mohammed Abed/AFP photo)
Prime Minister Benjamin Netanyahu told his cabinet on Sunday that Israel "will not engage in negotiations under fire".
The statement came shortly after the Palestinians warned they would leave Cairo if Israel refused to show up by 1300 GMT.
There was no let up in violence on the ground, where a 17-year-old boy was killed in an Israeli strike on central Gaza, medics said.
In Gaza City, all the shops were shuttered on Sunday with fear keeping people off the streets, but there was also a sense of deep frustration.
"We are tired. We just want to go home, but we want something in exchange for all our suffering," 27-year-old Samar Mohammad told AFP.
"I feel frustrated but I am confident that Israel will cave in and accept the demands of the resistance or Hamas will keep firing rockets until they do," said Shadi Abu al-Heytan, 35.
In the West Bank, medics said an 11-year-old Palestinian boy was killed in a shooting that witnesses accused Israeli soldiers of carrying out. The military said it was looking into the reports.
Hamas-linked mosques destroyed
The Cairo talks broke down on Friday after Hamas accused Israel of stalling and refused to extend a 72-hour ceasefire, setting off renewed hostilities that left eight Palestinians dead on Saturday as Israeli warplanes battered Gaza with 50 air strikes.
The United Nations says at least 1,354 of the Palestinians killed were civilians, including 447 children.
Mussa Abu Marzuq, deputy head of Hamas's exiled leadership, accused Israel of stalling over its demands and said Sunday would be crucial for deciding "the fate of the negotiations".
"We do not want an escalation, but we will not accept that there is no reply to our demands," he said late Saturday.
The Palestinian delegation, which includes Palestine Liberation Organisation officials as well as senior figures from Hamas and Islamic Jihad, was holding further talks with Egyptian mediators from 0800 GMT, an official said.
But there appeared little chance of a breakthrough.
"The prospects of reaching an agreement are weak and the Palestinian delegation could leave Cairo at any moment," Izzat al-Rishq, member of the Hamas politburo, tweeted shortly before the talks began.
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Meanwhile, Netanyahu held talks with his cabinet at the defence ministry in Tel Aviv, with hardliners exerting pressure him to send troops back into Gaza to topple Hamas, the de facto power in the battered Palestinian enclave.
Israel withdrew its forces from Gaza on August 5, wrapping up a nearly three-week ground operation aimed at destroying a network of cross-border attack tunnels.
"This situation cannot continue," Foreign Minister Avigdor Lieberman said ahead of the meeting.
"There is no doubt that the only thing left to do now is to overpower Hamas, clean out the territory and get out as quickly as possible."
A women with her baby prepares to leave her destroyed home amid ruins in the Shejaia neighbourhood in Gaza City. (Reuters Photo)
Interior minister Gideon Saar, another hardliner, agreed.
"What we must do is break the military power of Hamas in Gaza," he said, without elaborating.
Last week's pullout of Israeli ground troops and the subsequent three days of calm brought relief to millions after four weeks of bloody fighting which has killed more than 2,000 Palestinians and 67 in Israel, most of them soldiers.
UN figures show that nearly three quarters of the victims were civilians, with children making up around a third of the civilian death toll.
France, Britain and Germany on Saturday demanded an immediate halt to the ongoing hostilities in a joint declaration which said a ceasefire must address "both Israeli security concerns and Palestinian requirements regarding the lifting of restrictions on Gaza," it said.
Lifting Israel's eight-year blockade on Gaza is the main Palestinian demand at the truce talks.
On Saturday, a Palestinian official said they had agreed with Egypt on a draft proposal which would be handed to Israel.
It would see Egypt and the Palestinian Authority take control of the Rafah border crossing, while negotiations on the establishment of a sea port in Gaza, which Hamas has demanded, would then be delayed and entrusted to the PA, which - unlike the Islamist movement - has an interface with Israel.
Israeli troops kill Palestinian boy during West Bank clash
An 11-year-old Palestinian boy was shot dead by Israeli troops in a refugee camp in the southern West Bank on Sunday, relatives and Palestinian medics said.
Khalil Mohammed al-Anati had been playing outside his home at one end of Al-Fawwar refugee camp, southwest of the flashpoint city of Hebron, when an Israeli unit moved into the area, his uncle told AFP.
"We don't know what they (the Israelis) were doing," said Yussef al-Anati, crying, his shirt soaked in blood after carrying his nephew to hospital.
"Khalil was playing in front of the house, then we heard gunfire. The kid was screaming and fell down," he said. "He was shot in the back and the bullet exited through his stomach."
A medical official confirmed his death.
The Israeli military said it was looking into the reports.
Dozens of relatives and people gathered outside the morgue where the child's body was taken. The funeral was to be held later on Sunday.
Protesters fill London and Cape Town
Palestinian foreign minister Riyad al-Malki meanwhile said his government would soon try to haul Israelis before an international court for war crimes.
"We will go to the ICJ (International Court of Justice), and put our signature on it. Very soon we will be a (sovereign) state. That is enough for the court to start an investigation," Malki told AFP on a visit to Colombia.
In London, up to 150,000 protesters packed Oxford Street on Saturday, marching to the US embassy and on to Hyde Park, many of them chanting "Free, free Palestine" and holding up banners saying "UK -- Stop Arming Israel".
Tens of thousands of demonstrators also marched through Cape Town to protest the Israeli military operation, one of the biggest rallies in the city since the end of apartheid.
Smoke from an Israeli strike rises over Gaza City, Gaza Strip. (PTI Photo)
The lifting of Israel's land and sea blockade, imposed in 2006 after Hamas captured an Israeli soldier, has been a key demand of Hamas and the Palestinian Authority in the Cairo talks.
A Palestinian official said on condition of anonymity that Egypt and the Palestinians had reached a draft agreement for submission to Israel.
It would see Egypt and the Palestinian Authority take control of the Rafah border crossing into Egypt, essentially activating part of a unity accord Hamas signed with the PA in April.
Negotiations on the sea port, demanded by Hamas, would then be delayed and entrusted to the PA, with whom Israel is prepared to deal.
Israel waged the conflict to destroy Hamas's arsenal of rockets and its vast network of attack tunnels.
But combat has not resumed at the same fierce intensity, feeding hopes that a new truce could be agreed.
"Our hope is that the parties will agree to an extension of the ceasefire in the coming hours," US State Department spokeswoman Marie Harf said.
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Chris Gunness, spokesman for the UN agency for Palestinian refugees (UNRWA), called for the Gaza blockade to end so reconstruction can begin.
"Huge swathes of Gaza have been levelled. We cannot rebuild it with our hands tied behind our backs," he said. "The blockade must end."
At least 65,000 people have had their homes destroyed, and UNRWA said 222,000 people are still sheltering in UN-run schools.