Another 52 Palestinians have died, raising the toll from Israeli strikes on Gaza to 157, in the bloodiest day since the conflict erupted on Tuesday.
Palestinian militants fired more rocket salvos as both sides dismissed calls for a truce.
Israel continues to build up troops along the border ahead of a possible invasion, warning Palestinians in northern Gaza to evacuate.
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 full-scale conflict.
Israel’s aerial campaign saw strikes start early on Saturday, including a hit on a centre for the handicapped and another that killed two nephews of former Hamas premier Ismail Haniya.
Rockets fired from Gaza targeted Jerusalem and Tel Aviv, with some hitting two southern West Bank cities, but so far causing no Israeli deaths.
Late on Saturday night, an Israeli strike hit the Tuffah district in eastern Gaza City, targeting a home and a mosque and killing 16 people, emergency services 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 Tel Aviv.
Three rockets apparently targeting Jerusalem fell short, hitting Hebron and Bethlehem, the Israeli army and Palestinian security sources said.
Of four fired at Tel Aviv, three were intercepted above the city and another hit open ground south of it, the army said.
Over 500 rockets have struck Israel during the latest conflict, and on Saturday evening two rockets fired from Lebanon hit uninhabited areas in northern Israel, the army said.
Egyptian president Abdel Fatah al-Sisi’s government was in touch with both sides, his spokesman said.
He met Middle East Quartet envoy Tony Blair in Cairo on Saturday to discuss the crisis.
Washington has said it is willing to “leverage” its relationships to bring about a ceasefire as the chief diplomats of Britain, France, Germany and the US 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.
Israeli Prime Minister Netanyahu said on 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.
Some 33,000 Israeli reservists have been mobilised out of 40,000 approved by the cabinet.
Foreign Minister Avigdor Lieberman has said he expects a political decision on a possible ground operation to be taken by Sunday.