Gaza's Hamas rulers said they were ready for a fresh bid to rein in cross-border fighting with Israel, after medics said three Palestinians were killed in air raids on Saturday.
Hamas and "the Palestinian resistance factions will respect the truce as long as the (forces) of the occupation do the same, and that's what we told our Egyptian brothers who demanded that we cease fire," a Hamas leader, Ayman Taha, told AFP.
"The Egyptians have demanded that the (forces) of the occupation stop their aggression and have informed us that they are prepared to do so," he added.
"We told them that we shall respond to calm with calm; if the occupier stops (its attacks), there will be no further retaliation by the resistance factions."
An official close to the Islamist movement said a new Egyptian-brokered truce would take effect from midnight (2100 GMT).
Israeli Prime Minister Benjamin Netanyahu's office declined to comment but local media said neither side wanted an escalation, with Russian President Vladimir Putin due to start a rare visit to Israel and the Palestinian territories on Monday.
At a Saturday night meeting of the Revolutionary Council of his Fatah party Ramallah, Palestinian president Mahmud Abbas condemned "Israeli aggression" against Gaza and called for "a permanent return to calm".
Hamas earlier threatened to call off a previous truce attempt announced on Wednesday which was unravelling, with Palestinian officials reporting three Palestinians killed and dozens wounded in seven Israeli air strikes on Saturday.
And shortly after Taha's announcement, Palestinians fired another five rockets towards the southern Israeli coastal city of Ashkelon but all were intercepted by Israel's Iron Dome air defence system, the military said.
An army spokeswoman said that by Saturday evening 24 rockets had slammed into southern Israel from Gaza during the day, with 10 brought down by Iron Dome. Others were reported to have fallen at sea or inside the Gaza Strip itself.
A man in the town of Sderot was injured in one attack, Israeli police said.
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The current round of Israeli attacks and Palestinian retaliation began with air strikes Monday morning, just hours after gunmen from Sinai carried out an ambush along Israel's southern border with Egypt, killing an Israeli civilian.
Israel has said its sudden spike in Gaza operations was "in no way related" to the Sinai border incident, with the military saying the air force was targeting militants poised to attack the Jewish state.
Palestinians have since Monday reported 15 dead in Gaza strikes, with dozens wounded. At least 150 rockets and mortar shells have hit Israel, wounding five people, among them four border police officers.
Among Saturday's fatalities, Palestinian officials said, was six-year-old Ali al-Shawaf whose father and another man were wounded in the same strike, east of Khan Yunis. The Israeli military denied it was responsible.
"The explosion that caused the death of the Palestinian child today was because of ordnance belonging to one of the terror groups," Lieutenant Colonel Avital Leibovich, the army's foreign press spokeswoman, said on Twitter.
Also killed was Ussama Ali, 42, who medics said had been on his way to a wedding in a residential district of Gaza City when he was killed by a missile apparently aimed at a passing motorcyclist.
The rider was injured and taken to the city's Shifa hospital.
The Israeli military said that its air force carried out an attack in the northern part of the strip, where Gaza City is located, but it did not give the precise location.
The air force "targeted a terrorist squad... during final preparations to fire a rocket at Israel," it said in a statement. "A hit was confirmed."
Earlier in the day, Palestinian medics said, an Israeli drone killed a Palestinian man, Khaled al-Burai, 25, east of Jabaliya, in northern Gaza.
Witnesses said Israeli aircraft carried out at least four other strikes elsewhere in Gaza on Saturday. One targeted militants travelling in a car in the Zeitoun neighbourhood east of Gaza City after they had fired rockets into Israel, they said.
Raids also struck the Beit Lahiya area in the north and the Nusseirat and Al-Bureij refugee camps in central Gaza, without causing casualties, witnesses said.