Palestinian and Israeli officials are continuing indirect talks in Cairo on a long-term truce in Gaza as the three-day ceasefire enters its last 24 hours.
Israeli officials say they are willing to extend the ceasefire before it expires on Friday morning.
But Hamas, which controls Gaza, says there is no agreement and there is a big gap between the sides' positions.
The armed wing of Hamas has warned of renewed fighting if Israel does not end its blockade of Gaza's port.
Four weeks of fierce fighting between Israeli forces and militants in Gaza claimed more than 1,900 lives.
UN Secretary General Ban Ki-moon demanded an end to what he called the "senseless cycle of suffering" on Wednesday.
Egyptian officials, who brokered the 72-hour ceasefire that began on Tuesday, were working against the clock on Thursday to persuade both sides to agree a long-term deal.
"Indirect talks are ongoing and we still have today to secure this," an Egyptian official told Reuters news agency when asked whether the truce was likely to be extended beyond 08:00 (05:00 GMT) on Friday.
"Egypt's aims are to stabilise and extend the truce with the agreement of both sides and to begin negotiations towards a permanent agreement to cease fire and ease border restrictions."
On Wednesday, Israeli officials said they had expressed their readiness to "extend the truce under its current terms". But the deputy political leader of Hamas, Moussa Abu Marzouk, said: "There is no agreement."
Sally Nabil, BBC News, Cairo
Indirect negotiations between the Israelis and Palestinians are going on behind closed doors at a secret venue.
There is no media access and no-one is willing to make any official statements about the content of the discussions or their expected outcome.
We have only been able to contact the Palestinian delegation by telephone and they normally just re-iterate calls for the lifting of the blockade of Gaza, the release of prisoners and the end of the Israeli offensive.
The Israelis, for their part, are sticking firm to their main demand - the demilitarisation of Gaza. But this has been met with a big "no" from all the Palestinian factions.
Egyptian intelligence is the main mediator, but it faces a tough task. The gap between the Israelis and Palestinians will be hard to bridge.
The main Israeli demand for a long-term agreement is reportedly the demilitarisation of Gaza. Correspondents say that is highly unlikely to be accepted by Hamas, which considers itself a resistance movement and refuses to lay down its arms.
Hamas and the other Palestinian factions are meanwhile demanding an end to the blockade of Gaza and the freeing of prisoners released in exchange for Gilad Shalit in 2011 who were recently re-arrested. So far, there has been no public response from the Israelis.
Israeli offensive began
4,760+ air strikes on Gaza
3,488 rockets fired at Israel
1,973 people killed in Gaza
UN estimates +70% of deaths are civilians
3 civilians killed in Israel
64 Israeli soldiers killed
"Nobody accepts demilitarisation of the weapons in Gaza while the Israeli occupation is continuing and the siege on Gaza is continuing, and the crimes against our people are continuing," Palestinian official Wasel Abu Yousef told the Associated Press.
Israeli Communications Minister Gilad Erdan warned Palestinian militants not to disrupt the ceasefire, telling Israel Radio: "We are preparing for any situation and if they resume fire, the military will resume operations."
Palestinian officials say at least 1,875 people have been killed since Israel launched Operation Protective Edge on 8 July with the aim of halting rocket fire from militants in Gaza and destroying the network of tunnels it said were used by militants to launch attacks inside Israel.
The UN says 1,354 of those who died were civilians, including 415 children and 214 women.
Israel's government says 64 soldiers were killed, along with two Israeli civilians and a Thai national. It also claims that about 900 Palestinian militants were killed in the fighting.
On Thursday, the human rights group Amnesty International called for an investigation into what it said was mounting evidence that Israeli forces had deliberately attacked hospitals and health professionals in Gaza. The attacks have left at least six medics dead.
"Our ambulances are often targeted although they are clearly marked and display all signs that they are ambulances," said Dr Bashar Murad, director of Palestinian Red Crescent Society's (PRCS) emergency and ambulance unit, which lost at least two members of staff.
"The army should be able to distinguish from the air that what they are targeting are ambulances."
Amnesty International said attacks on health facilities and professionals were prohibited by international law and amounted to war crimes.
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