Israeli forces pounded multiple sites across the Gaza Strip on Wednesday, including the enclave's sole power plant, as diplomats sought to end the bloodshed.
In a blow to Israel's economy, US and European air carriers halted flights in and out of Tel Aviv citing security worries.
Israel urged a re-think, saying its airspace was safe.
US Secretary of State John Kerry was in Egypt and UN Secretary General Ban Ki-moon in Israel, spearheading international efforts to secure a ceasefire. Hamas ally Qatar was also working in the background to seek a solution.
Israel sent ground troops into Gaza last Thursday, looking to knock out Hamas's missile stores and destroy an underground network of tunnels.
630 Palestinians, many of them children and civilians have been killed in the Gaza offensive, including a seven-year-old hit by a shell in southern Gaza early Wednesday, a medic said.
31 Israelis, 29 of them soldiers, have died.
Clouds of black smoke hung over the densely populated Mediterranean enclave, with the regular thud of artillery and tank shells filling the air.
Dozens of Palestinian families trapped by the war on Gaza are scrambling to flee a southern Gaza Strip neighborhood as Israel reported that two more of its soldiers have died in the conflict, reported AP.
The Palestinian Red Crescent says it is trying to evacuate about 250 people from near Khan Younis, which has been under Israeli tank shelling and drones strikes since early Wednesday.
There was also violence in the occupied West Bank, where a Palestinian was shot dead by Israeli troops near Bethlehem. The army said soldiers fired a rubber bullet at him during clashes with Palestinians hurling rocks and Molotov cocktails.
The Palestinian decision-making body led by President Mahmoud Abbas on Wednesday endorsed demands by Hamas for halting Gaza hostilities with Israel, a closing of ranks that may help Egyptian-mediated truce efforts.
Hamas has baulked at Cairo's offer, saying it wanted assurances of relief from an Israeli-Egyptian blockade and other concessions. The dispute was further complicated by distrust between Egypt under President Abdel Fattah al-Sisi and Hamas.
In a move that could effectively turn Abbas into the main Palestinian point person for a Gaza truce, his umbrella Palestine Liberation Organization (PLO) on Wednesday formally supported core conditions set by Hamas.
Egyptian sources, speaking on Tuesday as top US diplomat Kerry visited Cairo to advance truce efforts, said a unified Palestinian position could help achieve a deal.
A senior Palestinian official said Tuesday talks were ongoing with Hamas for a truce to end its war in Gaza with Israel, adding both sides have refused a humanitarian ceasefire.
Azzam al-Ahmed, an aide to Palestinian president Mahmud Abbas, landed again in Cairo on Tuesday where he could meet US Secretary of State John Kerry.
Ahmed said they had recommended that the Egyptian proposal set a timetable of five days of talks after a ceasefire, although Hamas was still refusing."
According to the Egyptian proposal, negotiations (between Israel and Hamas) should start within 48 hours," he told reporters in Cairo.
Abbas's camp "fine-tuned this so the negotiations last for a duration of five days," he said, adding however that Hamas had shown no interest in this amendment.
"Hamas until now is sticking to its position. But we agreed to continue communicating with them, so we could perhaps agree on a final draft," he said.
Israel faced mounting international alarm at the civilian death toll, as well as increased economic pressure from lost tourism revenues after the US Federal Aviation Administration (FAA) took the rare step on Tuesday of banning flights to Tel Aviv's Ben-Gurion International Airport for at least 24 hours.
European airlines also cancelled flights to Israel, whose own carriers continued to operate.
An Israeli official said Netanyahu had asked Kerry to help restore the US flights. A US official said the Obama administration would not "overrule the FAA" on a security precaution but noted the ban would be reviewed after 24 hours.