The two sides huddled in an Egyptian government building for nine consecutive hours, a Palestinian official said Monday, in what are expected to be marathon negotiations in the coming days.
The Palestinian delegations were more optimistic Monday, the Palestinian official told The Associated Press, who spoke on condition of anonymity because he was not authorized to discuss the negotiations with the media. He said progress was made on several issues.
The 72-hour truce, brokered by Egypt, took effect just after midnight, in the second attempt to halt a month of heavy fighting between the sides.
A similar three-day truce collapsed on Friday when militants resumed rocket fire on Israel after the sides were unable to make any headway in Egyptian-brokered negotiations for a more lasting deal. Hamas is seeking an end to an Israeli-Egyptian border blockade, while Israel wants Hamas to disarm.
The monthlong war, pitting the Israeli military against rocket-firing Hamas militants, has killed more than 1,900 Palestinians, the majority civilians, Palestinian and U.N. officials say. In Israel, 67 people have been killed, all but three of them soldiers, officials there say.
The halt in violence allowed Palestinians in war-battered Gaza to leave homes and shelters.
On Monday morning, high school students in Gaza filled the streets as they headed to pick up their graduation certificates after the Education Ministry said they'd be ready. People waited to buy fuel for generators as power and communication workers struggled to fix cables damaged in the fighting. Long lines formed at ATMs.
Last week's talks failed in part because Israel rejected Hamas' demand for a complete end to the blockade of the Gaza Strip, enforced by Egypt and Israel. Israel says the closure is necessary to prevent arms smuggling, and officials do not want to make any concessions that would allow Hamas to declare victory.
The blockade has greatly limited the movement of Palestinians in and out of the impoverished territory of 1.8 million people for jobs and schooling. It has also limited the flow of goods into Gaza and blocked virtually all exports. Unemployment there is more than 50 percent.
Hamas officials have since signaled that they will have more modest goals in the current round of talks.
Bassam Salhi, a Palestinian delegation member, said he was optimistic ahead of Monday's talks.
"We hope to reach a deal within the 72 hours, based on ending the blockade and opening the crossings," Salhi said.
Israel's finance minister, Yair Lapid, called on the international community to offer a massive aid package for Gaza conditioned on the Western-backed Palestinian Authority returning to power in Gaza.
Hamas, which is shunned as a terrorist group by the West, ousted the forces of Palestinian President Mahmoud Abbas in 2007.
In an interview, Lapid said Abbas is the legitimate authority in Gaza, and that if Hamas were removed, the blockade could be lifted, achieving Hamas' own stated purpose for firing rockets.
"We think this is feasible, and we think we should involve the Arab world into the process, and we should involve the entire international community," he said. "The end is peaceful Gaza, a peaceful Israeli south, and a rehabilitated Gaza."
Palestinian officials said the two delegations met throughout the day, and into the evening, at an Egyptian intelligence facility in Cairo. Journalists were barred from the site, and there were no details on the talks.
The officials, speaking on condition of anonymity because they were not supposed to discuss the negotiations with the media, said the Egyptians told both sides to brace for marathon negotiations in order to reach a deal before the 72-hour window closed.
One of the officials told AP that he was optimistic after Monday's talks and that progress has been made in some of the key issues.
He said that Israel had accepted that the western-backed secular Palestinian Authority, which governs parts of the West Bank, be able to pay salaries of civil servants in Gaza that belong to Hamas. Salary payments for more than 40,000 government employees hired by Hamas during the past seven years are a key point of contention.
Progress had also been made on allowing building materials into Gaza for reconstruction purposes, he said.
Israeli officials could not immediately be reached for comment on the talks.
Israel's Channel 10 TV cited an unidentified Egyptian source as saying it would take more than 72 hours, meaning the temporary truce will have to be extended or there will be another return to fighting.
It said that Egypt had offered some opening of its Rafah border crossing with Egypt, but that Hamas was worried the opening would be partial. The crossing is Gaza's primary gateway to the outside world.
The report said there were also deep differences over Israel's demand for demilitarization of Gaza, and Hamas demands to reopen the territory's airport and seaport.
The current Gaza war escalated from the abduction and killing of three Israeli teens in the West Bank in June. Israel blamed the killings on Hamas and launched a massive arrest campaign, rounding up hundreds of its members in the West Bank. Hamas and other militants unleashed rocket fire from Gaza.
Associated Press writers Dan Perry in Jerusalem and Ibrahim Barzak in Gaza City, Gaza Strip, contributed to this report.