An Israeli air strike killed two Palestinians in Gaza on Sunday as militants kept up rocket fire, a day after an Egyptian call for an open-ended ceasefire to enable new truce talks.
The pace of Israeli raids was slower than Saturday when at least 60 strikes pounded Gaza, killing 10 Palestinians, mostly women and children, and bringing down a 12-storey apartment block.
But there was no immediate sign of either side adopting the ceasefire Egypt appealed for on Saturday to allow negotiators from the two sides to return to Cairo to thrash out the details of a durable truce.
Israeli aircraft hit 20 "terror targets" in Gaza during the morning, while militants fired at least 20 rockets or mortar rounds at Israel, the army said.
An Israeli strike on the western side of Gaza City killed two Palestinians and wounded five, emergency services said.
Since a previous round of frantic Egyptian diplomacy collapsed last Tuesday, shattering nine days of calm, 88 Palestinians and a four-year-old Israeli boy have been killed in the violence.
In its statement on Saturday, the Egyptian foreign ministry called on "concerned parties to accept a ceasefire of unlimited duration and to resume indirect negotiations in Cairo".
Previous ceasefires with fixed timeframes have failed to give Egyptian mediators shuttling between Israeli and Palestinian negotiating teams enough time to broker a deal acceptable to both sides.
Israel insists on full safety for millions of citizens who live in daily fear of rocket fire.
Gaza's Islamist de facto ruler, Hamas, says any truce must provide for a lifting of Israel's crippling eight-year blockade of the territory and the opening of a seaport and airport.
Saturday's pounding by the Israeli air force came after Prime Minister Benjamin Netanyahu promised harsh retribution for the death of the Israeli child in a rocket strike on a kibbutz near the Gaza border.
But on Saturday, Defence Minister Moshe Yaalon told community leaders in the south that Israel now needed to look for a diplomatic solution to the rocket fire, adding that it would be doing so from a position of strength.
"I am convinced the other side in its condition needs a ceasefire more than we do," Yaalon said.
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"We need to see that we direct things diplomatically... to a place in which we'll achieve quiet and security for a longer period," he said.
The invitation to new truce talks came after a meeting on Saturday between Egyptian leader Abdel Fattah al-Sisi and Palestinian president Mahmud Abbas.
"What interests us now is putting a stop to the bloodshed," Abbas said.
"As soon as a ceasefire goes into effect, the two sides can sit down and discuss their demands," he said, adding that, as in previous rounds of talks, Hamas would be represented in the Palestinian delegation.
Hamas spokesman Sami Abu Zuhri told AFP that "any proposal offered to the movement will be discussed".
Abbas held two rounds of talks in Qatar on Thursday and Friday with exiled Hamas leader Khaled Mehaal before heading to Cairo.
At least 2,105 Palestinians and 68 people on the Israeli side, all but four of them soldiers, have been killed since the conflict erupted on July 8.
The UN says 70 percent of the Palestinians who have died were civilians, and that among the dead were 478 children.
Around 460,000 people have fled their homes in Gaza -- more than a quarter of the enclave's 1.8 million population.
On Sunday, five rockets fired from Syrian-controlled territory slammed into the Israeli-occupied sector of the Golan Heights but caused no casualties, the Israeli army said.
An army spokeswoman told AFP that it was not known who launched the rockets and the Israeli military did not return fire.
Late Saturday, a rocket fired from Lebanon struck northern Israel, causing damage but no casualties, police and the army said.
No group took responsibility for what appeared to be a show of support for Hamas, in an act similar to rocket launches from Lebanon last month.