It was the bloodiest day since the conflict erupted on Tuesday, with 46 Palestinians killed.
Both sides have dismissed calls for a truce, and Israel continued to build up troops along the Gaza border ahead of a possible ground invasion, warning Palestinians in northern Gaza to evacuate their homes.
With the Palestinian death toll at 151, and with no Israelis killed, the UN Security Council unanimously urged Israel and Hamas to respect "international humanitarian laws" and stop the loss of life.
The 15-member council urged a return to "calm, and restitution of the November 2012 ceasefire", referring to Gaza's last deadly full-scale conflict.
Israel's aerial campaign -- the largest and deadliest since 2012 -- saw strikes start early on Saturday, including one that hit a centre for the handicapped, and another that killed two nephews of Gaza's former Hamas premier, Ismail Haniya.
Rockets fired from Gaza targeted Jerusalem and Tel Aviv, with several intercepted over Israel's commercial capital and Jerusalem-bound projectiles hitting two southern West Bank cities.
Hundreds of rockets have so far caused no Israeli deaths, and many have been intercepted by the Iron Dome missile defence system.
- Centre for disabled hit -
An attack on the northern Gaza Strip hit a centre for the handicapped, killing two disabled women and wounding four, the centre's director said.
"They didn't understand what was happening and they were so frightened," Jamila Alaywa said of those inside the care home.
"They fired the rocket and it hit us without any warning."
Later on Saturday night, an Israeli strike hit the Tuffah district in eastern Gaza City, targeting a home and a mosque and killing 16 people, medics said.
Among the wounded was police chief Tayseer al-Batsh, officials said.
Hamas unleashed a barrage of rocket fire after issuing a rare warning that it planned to fire at the Israeli city of Tel Aviv.
Three rockets apparently targeting Jerusalem fell short, hitting Hebron and Bethlehem, the army and Palestinian security sources said, with no reports of casualties.
Of four fired at Tel Aviv, three were intercepted above the city and another hit open ground south of it, the army said.
Well over 500 projectiles have struck Israel during the conflict, and on Saturday evening two rockets fired from Lebanon hit uninhabited areas in northern Israel, the army said.
Israel responded with artillery fire.
Amid international efforts to mediate a truce, Egyptian president Abdel Fatah al-Sisi's government was in touch with both sides, his spokesman said.
Sisi met Middle East Quartet envoy Tony Blair in Cairo on Saturday to discuss the crisis, and later warned any escalation would cause further loss of "innocent lives".
Washington has said it is willing to "leverage" its relationships in the region to bring about a ceasefire.
The chief diplomats of Britain, France, Germany and the United States are due to discuss how to achieve a truce when they meet in Vienna on Sunday.
Italian Foreign Minister Federica Mogherini plans to visit Israel and the Palestinian territories from July 14-17 and Egypt on July 18, her ministry said.
- Little sign of compromise -
However, there has been little sign that either side is interested in an immediate end to the hostilities, which appeared to be ramping up on Saturday.
The Israeli army said it was sending messages to residents of northern Gaza "urging them to leave their homes for their own safety."
"It's unsafe to be near Hamas," it said.
On Friday, Cairo said its efforts to mediate a return to a 2012 ceasefire agreement "have met with stubbornness".
And Israeli Prime Minister Netanyahu said Friday that "no international pressure will prevent us from striking, with all force, against the terrorist organisation which calls for our destruction."
Hamas's Haniya sounded a similar tone, saying: "(Israel) is the one that started this aggression and it must stop, because we are (simply) defending ourselves."
The latest conflict unfolded after last month's kidnap and murder of three young Israelis in the occupied West Bank and the brutal revenge killing of a Palestinian teenager by Jewish extremists.
Israel cracked down on Hamas, though the Islamist group declined to confirm or deny involvement in the abductions, and Gaza militants hit back with intensified rocket fire.
Israel says preparations are under way for a possible ground incursion, with tanks and artillery massed along the border and some 33,000 reservists mobilised out of 40,000 approved by the cabinet.
Foreign Minister Avigdor Lieberman has said he expected a political decision on a possible ground operation to be taken by Sunday.
