Palestinian factions have agreed to a new 72-hour ceasefire in Gaza, Egyptian state TV has reported as negotiating teams in Cairo struggled to keep indirect Israeli-Palestinian peace talks alive. Israel is yet to respond.

Efforts to reach an agreement have faltered since Hamas its negotiating team in Cairo had been offered nothing in return for peace. A Palestinian source said that a new 72-hour ceasefire is under discussion, though no final decision has been made.

But a senior member of the Palestinian delegation in Cairo, Azzam al-Ahmad, said his team were willing to stay and negotiate indirectly with Israel, via Egyptian mediators, despite earlier suggestions that the Palestinians were close to abandoning the process.

On Saturday, the Palestinian delegation also threatened to withdraw, again saying Israel had not responded to any of their demands. By mid-afternoon local time, no decision had been announced, nor was there any confirmation of repeated reports of a new ceasefire.

Analysts now fear a long and lethal period of continued violence in Gaza, that would exacerbate a grave humanitarian crisis in the overcrowded region and curtail any bid to repair the colossal damage done to the infrastructure of Gaza in the month-long conflict.

"If today's efforts are going to fail, as looks likely, we are going to see a long war of attrition," said Mkhaimar abu Sada, a Gaza-based political analyst. Around half a million people in Gaza have been forced out of their homes, with more than 200,000 now living in United Nations schools. Roads, the water supply, sanitation systems as well as power generation and distribution networks have all been badly damaged. At least 60,000 are homeless.

Following renewed rocket and mortar fire from Gaza on Friday, Israel withdrew from the talks. Binyamin Netanyahu, speaking before a cabinet meeting on Sunday, said Israel would not negotiate "under fire".

He said: "The [military] operation will continue until its goal is met – the restoration of a quiet for a long period … The operation will take time and patience. … Israel will continue to take all action in order to change the current reality and bring quiet to all of its citizens."

Israel's communications minister, Gilad Erdan, told Channel 2 "a wide ground incursion and the toppling of Hamas is being discussed". Israeli air strikes and shelling killed five Palestinians in Gaza on Sunday, including a boy of 14 and a woman, officials said.

More than 1,900 Palestinians, mostly civilians, have died in the most deadly round of fighting between Israel and Hamas since the group seized control of Gaza in 2007, a year after winning a surprise victory in Palestinian elections. Three civilians in Israel have been killed, and 64 soldiers.

No Israeli casualties have been reported since Friday when two were hurt by mortar fire. The rockets being fired from Gaza since the end of the most recent ceasefire – the seventh since the start of the war – have all been short-range. More than 3,000 rockets have targeted Israel since tensions rose in June.

Sada described a stalemate. "Hamas is not going to defeat Israel. Israel is not interested in reoccupying Gaza which would be a nightmare for them. So both sides will try to exhaust each other. But this will be a disaster for Palestinians."

Saeed al-Saoudi, the head of civil defence in Gaza, said the continuing hostilities were causing problems for teams trying to clear rubble, retrieve the remains of casualties from strikes in recent weeks and restore basic services. "Three of our eight ambulances have been destroyed and two fire trucks. We have no ladders, no search equipment and we have had 36 people killed from my department."

In the restive West Bank, which has seen major demonstrations in recent weeks, an 11-year-old Palestinian boy was shot dead by Israeli troops in a refugee camp on Sunday morning, relatives and Palestinian medics said. Khalil Mohammed al-Anati had been playing outside his home at one end of al-Fawwar refugee camp, south-west of the flashpoint city of Hebron, when an Israeli unit moved into the area, his uncle told AFP.

Yussef al-Anati said: "We don't know what they [the Israelis] were doing", 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 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.

In an interview with the Guardian on Saturday night, Hamas's deputy chairman and one of the lead negotiators, Moussa Abu Marzouk, said that the Palestinian delegation would decide on Sunday whether or not to leave Cairo – where they have negotiated indirectly with their Israeli counterparts for a week. "There will be a meeting in order to decide if we are going to continue the talks or not – because there is no seriousness from the Israeli side about the talks."

Earlier, Hamas officials in Gaza threatened a major escalation of rocket strikes against Israel. Ihab al-Ghussein, the Islamist organisation's deputy information minister, said that "if on [Sunday] we have no response to our demands, our defensive measures will be intensified". Hamas demands centre on ending an eight-year blockade of the Gaza strip, that has sent unemployemnt soaring and living standards plunging.

Marzouk also claimed that the Israeli delegation had made no attempt to negotiate since the end of a temporary ceasefire on Friday morning, when the Israeli team flew back to Jerusalem to observe the Jewish sabbath, and did not return. He said Hamas had not made a final decision about escalating its own attacks on Israel – should the talks fail – but claimed that "all the options are available to the Palestinian people in order to them to gain their rights". He added: "If we don't have justice and rights, we will keep resisting our enemies until we get them … If they don't give us our rights today, we will continue the battle."

The concession Hamas most wanted from Israel, Marzouk said, was the right to build a port and airport in Gaza, facilities promised to the Palestinians under the Oslo peace deal. In return, he said Hamas had no problem with relinquishing power to a Palestinian Authority-led unity government that "should control everything in Gaza", including its border crossings.

A deal establishing a unity government was signed in June. However Hamas officials have repeatedly said that disarmament was out of the question. "It's not on the negotiation table. There is no force that can take away from the Palestinian resistance their right to resistance, nor their tools to resist," Marzouk said.

Speaking in Gaza on Sunday, Mustafa Barghouti, a veteran Palestinian politician and activist, questioned a "unilateral ceasefire while [Israel] has planes flying all over Gaza. Netanyahu is trying to impose a new status quo … Why should disarmament only be on one side? Israel is not trying to disarm Hamas but the Palestinian people."

Meanwhile, some Israeli hardliners actually called for an intensification of Israel's military operations. Avigdor Lieberman, the foreign minister, said: "This situation cannot continue.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."

The interior minister, Gideon Saar, another hardliner, said Israel needed to "break the military power of Hamas in Gaza".