The second extension of the ceasefire, this time for five days rather than three, has raised hopes that a longer-term resolution to the conflict can be found, although the way ahead remains fraught with difficulty.
A senior Hamas official who returned to Gaza from the negotiations in Cairo said they had been tough but expressed some optimism.
"There is still a real chance to clinch an agreement," Khalil al-Hayya told reporters, saying that it depended on Israel not "playing with language to void our demands".
"The Egyptian mediators are entering a good effort and we wish them success in this negotiation battle."
After more than a month of intense conflict, which killed 1,945 Palestinians, many of them civilians, as well as 64 Israeli soldiers and three civilians in Israel, there is little appetite on either side for a resumption of bloodshed.
Hamas and its allies want an end to the Israeli and Egyptian blockade on Gaza. But Israel and Egypt harbour deep security concerns about Hamas, the dominant Islamist group in the small, Mediterranean coastal enclave, complicating any deal on easing border restrictions.
LIFTING THE BLOCKADE?
Hamas leader Ismail Haniyeh told Al-Aqsa Hamas television on Wednesday that Hamas would insist on "lifting the Gaza blockade" and reducing restrictions on the territory's 1.8 million people's movements as a prerequisite to a "permanent calm".
Members of the Palestinian delegation said they would return to Cairo for more talks on Sunday.
Israel's security cabinet, which has determined the course of the Gaza conflict, was scheduled to meet later on Thursday to discuss the proposals being put forward by the Egyptians.
Egyptian and Palestinian sources said Israel had tentatively agreed to relax curbs on the movement of people and goods across the border, subject to certain conditions.
A Palestinian demand for a Gaza sea port and reconstruction of an airport destroyed in previous conflicts with Israel has been a stumbling block, with Israel citing security reasons for opposing their operation.
The sides have agreed to delay discussion of any agreement on the ports for a month, a Palestinian official said.
As part of Egypt's blueprint, Israel would expand the area where it allows Gaza's fishermen to operate to six miles (10 km) from the shore, from three miles (5 km) at present.
EXPANDED FISHING ZONE
"It will increase gradually to no less than 12 miles in coordination between the Palestinian Authority and Israel," the official said, noting that any deal is likely to foresee an expanded role in Gaza for Western-backed Palestinian President Mahmoud Abbas.
Abbas's Fatah group, based in the occupied West Bank, formally ended a seven-year rift with Hamas in April, allowing the formation of a Palestinian unity government under Abbas.
The Egyptian plan would also reduce the size of a "no-go" area for Palestinians on the Gaza side of the border from 300 metres (330 yards) to 100 metres, so that local farmers can recover plots lost during security crackdowns.
Israel and Hamas have not met face-to-face in Cairo: Israel regards Hamas, which advocates its destruction, as a terrorist group.
Israel launched its military campaign on July 8 and declared its aim was to quell cross-border rocket fire from Gaza and destroy tunnels used by militants.
Most of the nearly 2,000 Palestinian dead have been civilians, hospital officials in the densely populated enclave say.
The heavy civilian losses and the destruction of thousands of homes in Gaza - where the United Nations said 425,000 of a population of 1.8 million had been displaced by the war - have stoked international alarm.
Israel pulled ground forces out of Gaza last week, saying the army had completed its main mission of destroying more than 30 tunnels dug by militants for cross-border ambushes. It now wants guarantees that Hamas will not use any reconstruction supplies sent into the enclave to rebuild the tunnels.