Indirect negotiations are being held in Cairo between Israel and major Palestinian factions, including Hamas.
It is the longest ceasefire yet since the war broke out last month in the Gaza Strip.
The fighting has killed more than 1,900 Palestinians, the majority civilians. Israel has lost 67 people, all but three of them soldiers.
Violence briefly spiked as the extension of a previous 72-hour truce was announced shortly before midnight on Wednesday. The extension is to last until midnight on Monday.
Israel’s military said eight Hamas rockets were launched at Israel but that the firing stopped in the early hours of yesterday. Israel retaliated with air strikes on rocket-launching sites in Gaza, its military said.
Gaza police said they recorded 17 Israeli strikes but that no casualties were reported.
Palestinian negotiators in the Egyptian capital expressed optimism that a sustainable road map for the war-torn territory could soon be achieved.
Senior Hamas negotiator Khalil al-Haya said: “There is a real opportunity to reach an agreement, but [Israel] must stop the manoeuvres and playing with words. We are not interested in more destruction for our people. We are not interested in more bloodshed.”
Hamas is seeking an end to a crippling blockade imposed by Israel and Egypt in 2007. The blockade has greatly limited the movement of Palestinians in and out of the territory and restricted the flow of goods.
Israel says the closure is necessary to prevent arms smuggling, and officials are also reluctant to make concessions that would allow Hamas to declare any kind of victory.
Israel wants Hamas to disarm, or at least be prevented from re-arming. Hamas has recovered from previous rounds of violence, including a major three-week ground operation in January 2009 and another week-long air offensive in 2012. It now controls an arsenal of several thousand rockets, some with long ranges and heavy payloads.
Mr Haya told reporters in Cairo Hamas would seek international guarantees to enforce any agreements reached with Israel. He said that together with the Palestinian Authority, which runs the West Bank and with which Hamas formed a unity government this year, the militant group would expect to play an important role in any Gaza reconstruction. The “national unity government is required to carry out its duty with regard to reconstruction”, he said.
Hamas negotiators left Cairo yesterday and flew for consultations with Hamas leaders in the Qatari capital, Doha.
It was the first time that Hamas figures were allowed to fly directly from Cairo airport since a military-backed government took over in Egypt last year, replacing Islamist president Mohamed Morsi, whose Muslim Brotherhood group was allied to Hamas.
The move appeared to reflect a recognition on Egypt’s part of Qatar’s importance in the talks.
Egypt has positioned itself as the key mediator in the talks, but its tough anti-Hamas policies could limit its effectiveness.
The tiny Gulf Arab nation of Qatar is seen as a conduit for Hamas demands. It hosts several Hamas leaders and has staunchly opposed the Egypt-Israel blockade of Gaza.