Gaza conflict: Mahmoud Abbas urges fresh talks in Egypt
Palestinian President Mahmoud Abbas has called on Israel and Hamas to attend fresh talks in Egypt.
The Egyptian foreign ministry said it was ready to mediate and called for an immediate ceasefire.
A previous Egyptian-brokered truce collapsed on Tuesday. Health officials said at least 10 Gazans were killed on Saturday, including two children.
Another 22 were hurt as a 12-storey block, said by Israel to be a Hamas command centre, was demolished.
More than 2,090 Palestinians - mostly civilians - and 67 Israelis have been killed in recent weeks.
Most of the dead on the Israeli side have been soldiers. A Thai national in the country was also killed by rocket fire early on in the six-week-old conflict.
Israel says that since the latest ceasefire ended, over 525 rockets have been fired into Israel from Gaza, with 69 of them intercepted by its Iron Dome anti-missile defence system.
The Israel Defence Forces (IDF) said it had carried out around 60 air strikes over Gaza on Saturday, while more than 70 rockets and mortar rounds fired from Gaza struck Israel.
The military added that a missile had also been launched from Lebanon and hit the Upper Galilee region, while at least five rockets fired from Syria hit different locations across the Golan Heights.
In Saturday's Gaza offensive, a 12-storey apartment building in Gaza City collapsed after being struck by two Israeli missiles. At least 22 people, four of them children, were injured in the attack, according to Palestinian health officials.
Israel said Hamas militants were using the building as a command centre.
Prior to starting the raids on Saturday, the IDF dropped leaflets over Gaza warning residents it would "continue to attack every area from which terror activities against Israel originate".
"Every house from which military activity is carried out, will be targeted. For your own safety, prevent terrorists from utilising your property for terror agendas," the leaflet goes on.
On Friday, a four-year-old Israeli boy was killed in a village near the Gaza border, prompting Israel to warn it would "intensify" its operations.
In an interview with Yahoo News, Hamas leader Khaled Meshaal rejected the charge that his organisation targets Israeli civilians.
"We try most of the time to aim at military targets and Israeli bases," Mr Meshaal said. "But we admit that we have a problem. We do not have the weapons available to our enemy… so aiming is difficult."
He also addressed the kidnapping and killing of three Israeli teenagers in the West Bank that helped precipitate the current crisis.
He said Hamas's leadership "were not aware of this action taken by this group of Hamas members in advance".
"We learned about these confessions from the Israeli investigation," he said.
A Palestinian teenager from East Jerusalem was abducted and burned alive in an apparent revenge attack two days after the bodies of the Israeli teenagers were found on 30 June.
The killings set off an escalating cycle of violence which led to the current conflict. Egyptian efforts to achieve a long-term ceasefire deal have so far been scuppered.
Hamas has insisted on a lifting of the economic blockade of Gaza as part of any longer-term deal.
Israel has vowed to pursue its campaign until "full security" is achieved through the disarmament of Hamas and other groups in Gaza.