Millions in Gaza and southern Israel have welcomed an extension to a temporary truce despite a rocky start which saw a flurry of rocket fire and air strikes.

Egyptian mediators brokered a five-day extension to an existing truce to allow for further negotiations on a long-term ceasefire to fighting that has killed 1,962 Palestinians and 67 people on the Israeli side since July 8.

Despite a series of overnight rocket attacks on Israel and Israeli air strikes on Gaza, the calm held throughout Thursday even if great uncertainty persists on both sides about the future.

Around 10,000 Israelis poured into Rabin Square in Tel Aviv late on Thursday, police said, calling on the government and the army to end Palestinian rocket attacks from Gaza once and for all.

It was the first major demonstration in Israel since the fighting began and organisers said it united people across often bitter divides of left and right-wing.

Members of the crowd waved Israeli flags and held up banners calling for peace with the Palestinians and others scrawled with the words: “Occupy Gaza now!”

The Israeli army said six Palestinian rockets struck Israel during the night, including three after the new truce came into effect at midnight.

Israeli warplanes hit back with four air strikes, Palestinian security officials told AFP, saying the skies fell silent at around 3:00 am (1000 AEST).

The Egyptian foreign ministry said both sides had agreed to extend the ceasefire for five days to allow more time for thorny negotiations.

Palestinian chief negotiator Azzam al-Ahmed said the delegations had reached “agreement on many points” concerning the lifting of Israel’s eight-year blockade on Gaza but needed more time to settle a number of remaining disputes.

Israel confirmed it accepted the Egyptian proposal.

Israeli negotiators and various members of the Palestinian delegation have left Cairo for consultations with their respective bases and are not expected to return before Saturday night at the earliest.

The Israeli security cabinet met on Thursday and discussions were expected to continue on Friday.

Speaking to reporters in Gaza City, Hamas politburo member Khalil al-Haya said there was “still a real chance of reaching an agreement”, but only if Israel “would stop playing with words”.

If observed, the latest truce should herald potentially the longest period of calm in the five-week conflict. An earlier truce collapsed in a firestorm of violence on August 8.

Egyptian mediators have proposed that talks on a seaport and airport in Gaza be delayed until a month after a permanent ceasefire takes effect, according to documents seen by AFP.

Negotiations over the exchange of the remains of two dead Israeli soldiers for the release of Palestinian prisoners held by Israel would also be postponed.

An Israeli-imposed buffer zone inside the Gaza border would be gradually reduced, and eventually policed by forces under the command of Palestinian president Mahmud Abbas.