CAIRO (Ma'an) -- The Palestinian and Israeli delegations resumed indirect negotiations in Cairo on Tuesday, the head of the Palestinian delegation said.
"We have to use every minute of the next 24 hours to reach an agreement or else the cycle of violence will continue," Azzam al-Ahmad told reporters.
Israeli and Palestinian negotiators agreed to extend a five-day ceasefire for another day just hours before it was set to expire at midnight Monday.
Palestinian sources in Cairo had told Ma'an earlier Monday that a long-term ceasefire agreement was being finalized after 15 days of Egypt-sponsored negotiations.
But al-Ahmad and other members of the Palestinian delegation denied the claims, warning that if Israel refused to make concessions, negotiations could collapse, leading to a resumption of hostilities in Gaza.
The talks in Cairo center on an Egyptian proposal that meets some of the Palestinian demands, but defers debate on other thorny issues until later.
The Egyptian proposal calls for both sides to immediately cease fire, and includes provisions relating to opening the borders to allow for free movement of people, goods and construction materials, as well as a clause on regulating the financial crisis within the enclave.
But crucially, it postpones discussions on difficult issues such as a port and airport in Gaza for another month "after calm and stability returns," along with talks over exchanging the remains of two Israeli soldiers presumed held by Hamas for the release of Palestinian prisoners.
The Palestinian delegation has insisted that any long-term truce include the end of Israel's eight-year siege on the Gaza Strip, the release of dozens of prisoners rearrested by Israel after being released in 2011, the re-opening of a seaport and airport in Gaza, and the creation of a safe passage between the West Bank and the Gaza Strip.A ceasefire 'for always'
Although the back-to-back truce agreements have brought relief to millions on both sides of the border, the drawn-out waiting and the fear of a resumption of fighting was beginning to test people's patience.
"No one here has any hope," said Riyad Abul Sultan, a father-of-10 with thick curly hair, smoking as he sits on a flimsy mattress at a UN school in Gaza.
"Maybe they'll finish the war for two hours, maybe Israel will start bombing again."
"We want a ceasefire for always, not for three days or for three days," agreed his wife, Wafa.
"The Israelis are enjoying some quiet. But me, my house is destroyed and I'm living with my husband and my kids in a UN school," snapped Manal Abu Abed, 40.
"Let them either kill us or let us live with some dignity!"
On Monday evening, a senior member of the Palestinian delegation insisted there had been "progress" on agreeing a more durable ceasefire, with both sides demonstrating "a great degree of flexibility."
Meanwhile, Gaza's health ministry said the death toll from Israel's month-long assault on the Strip rose above 2,000 as more people succumbed to injuries and bodies were found under rubble. The figures showed 2,016 people had been killed and another 10,196 wounded.
Among the dead were 541 children, the ministry said.
Israel has countered that any agreement should include the demilitarization of the Gaza Strip.AFP contributed to this report.