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Azzam Ahmed, a senior Fatah official, told reporters after a day of intense talks mediated by Egyptian intelligence that the Palestinians hoped to reach a final deal in the coming weeks, with Arab and international backing.
An Egyptian Foreign Ministry statement confirmed that a five-day extension to the ceasefire had been agreed.
Speaking as an existing 72-hour truce expired, Ahmed said that agreement had been reached on many issues but a few key sticking points remain, including on security.
"I say yes, there was progress and agreement on many of the sticking points," said Ahmed. "We hope that when we return in five days, this will be the final period to announce an agreement ... for a permanent ceasefire that ends the aggression against Gaza."
The Palestinian team expects to head to Ramallah on Thursday for consultations with Fatah leader Mahmoud Abbas, before returning to Egypt on Saturday to resume talks, several Palestinian officials said.
The Palestinians have called for an end to Israel's blockade of Gaza, the release of prisoners and the opening of sea and air ports as well as the expansion of fishing rights. Israel wants Gaza militants to disarm and their tunnels to be destroyed.
Ahmed said an Israeli demand for the disarmament of Gaza after the month-long war had not been discussed.
"For the atmosphere of calm to remain, there needs to be progress on some of the other details related to ... the lifting of the sea and air blockade," Azzam said.
He said more progress was also needed on issues including security and the role of the United Nations and the international community in any agreement.
Ahmed said a donor conference to rebuild Gaza would be hosted by Egypt, which has long sought the position of broker in Gaza, but has struggled to bring a lasting end to the fighting.
Though he said progress had been made, all sides in the talks have been reticent about the details and it was not clear how much of a gap still remained between the parties.
Another member of the Palestinian delegation said all issues remained up for discussion. An outbreak of fighting as the truce expired raised the possibility that the new ceasefire would collapse before it had properly begun.