A truce that has largely tempered a five-week war in Gaza was renewed last night, but the deal got off to a shaky start with rockets from Gaza hitting Israel and Israel retaliating with air strikes.
The Israeli military said Gaza militants breached the truce and fired eight rockets at Israel and that in response army forces targeted "terror sites" across Gaza.
There were no casualties reported in any of the incidents.
Hamas denied involvement in firing the rockets and accused Israel of violating the truce, extended at the last minute by another five days for the sides to work out a long-term ceasefire mediated by Egypt.
Israel had no comment on the new truce deal announced in Cairo by the Palestinians.
Hamas official Izzat Reshiq denied the Palestinians had breached the truce, and denounced Israel's air strikes as "a violation of the calm".
The halt in fighting, which has killed more than 2,000 people, had been set to expire at midnight.
Bridging the gaps between Israel and the Palestinians in order to secure a permanent ceasefire have proven difficult.
Hamas and its allies want an end to the Israeli and Egyptian blockade on Gaza.
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.
Hamas leader Ismail Haniyeh told Al-Aqsa Hamas television that the group would insist on "lifting the Gaza blockade" and reducing movement restrictions on the territory's 1.8 million residents, as a prerequisite to a "permanent calm".
Members of the Palestinian delegation said they would return to Cairo on Saturday night to begin more talks on Sunday.
A Palestinian official with knowledge of negotiations in Cairo said Egypt had presented a new proposal for a permanent truce.
Egyptian and Palestinian sources said Israel had tentatively agreed to allow some supplies into Gaza and relax curbs on the cross-border movement of people and goods, subject to certain conditions.
A Palestinian demand for a Gaza seaport and reconstruction of an airport destroyed in previous conflicts with Israel has also 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 the Egyptian blueprint, Israel was expected to expand fishing limits it imposes on Gaza fishermen to 10km from the usual 5km offshore zone.
"It will increase gradually to no less than 12 miles in coordination between the Palestinian Authority and Israel," the official said, referring to a likely expanded role in Gaza for Western-backed Palestinian President Mahmoud Abbas, based in the occupied West Bank.
In addition, the official said, the Egyptian plan calls for reducing the size of a "no-go" area for Palestinians on the Gaza side of the border from 300m to 100m 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.
The Gaza hostilities have killed 1,945 Palestinians and 67 on the Israeli side. Most of the Palestinian dead have been civilians.
Israel started its military campaign on 8 July to quell cross-border rocket fire from Gaza.
The heavy losses among civilians and the destruction of thousands of homes in Gaza - where the United Nations said 425,000 of a population of 1.8 million have been displaced by the war - have stoked international alarm.
Israel pulled ground forces out of Gaza last week after it said the army had completed its main mission of destroying more than 30 tunnels dug by militants for cross-border ambushes.
It now wants guarantees Hamas will not use any reconstruction supplies sent into Gaza to rebuild the tunnels.