THE Palestinian death toll in the Israeli offensive in the Gaza Strip has risen above 500 as the army said it had killed 10 militants who tunnelled into Israel, while Gazan officials said an Israeli tank shelled a hospital, killing civilians.

A day after he was caught by an open microphone saying sarcastically that the Israeli assault was "a hell of a pinpoint operation", US Secretary of State John Kerry flew to Cairo to try to secure an end to the two-week conflict.

Despite a UN Security Council appeal for an immediate ceasefire in the worst bout of Palestinian-Israeli violence for more than five years, neither the Palestinian Islamist group Hamas nor Israel appeared ready to stop fighting.

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Hamas, which killed 13 Israeli soldiers in Gaza on Sunday in the biggest one-day toll for eight years, continued to fire rockets deep into Israel yesterday and to dispatch infiltrators.

Israeli jets, tanks and artillery constantly pounded the densely-populated coastal strip, killing 28 members of a single family at the southern end.

At Al-Aqsa hospital in the central Gaza Strip, four people were killed and 70 wounded when an Israeli tank shell slammed into the third floor, housing operating theatres and an intensive care unit, the Health Ministry said. The Israeli military has accused Hamas militants of firing rockets from the grounds of Gaza hospitals and seeking refuge there.

The Palestinian death toll is now 518, including almost 100 children, since fighting started on July 8, say Gaza health officials. Israel says 18 of its soldiers have also died along with two civilians.

Hamas announced late on Sunday it had captured an Israeli soldier in Gaza, displaying a photo ID card and serial number, but there was no confirmation from the Israeli side.

Gilad Erdan, a member of Israeli Prime Minister Benjamin Netanyahu's inner security cabinet, said: "This is not the time to talk of a ceasefire. We must complete the mission and the mission cannot end until the threat of the tunnels is removed."

Two groups of Palestinian fighters had crossed from Gaza via two tunnels in the early morning, opening fire as they entered. Black and white surveillance footage supplied by the Israeli army showed one group of five or six men crouching and firing in long grass. Seconds later they were hit by a large explosion,. A military spokeswoman said at least 10 militants died.

For its part, Hamas, weakened by the loss of Egypt and Syria as allies, voiced determination to fight on to break a blockade on Gaza imposed by Israel and Egypt.

President Barack Obama repeated Israel had the right to defend itself against rocket attacks from Hamas militants but added: "We have serious concerns about the rising number of Palestinian civilian deaths and the loss of Israeli lives. That is why it now has to be our focus and the focus of the international community to bring about a ceasefire that ends the fighting and that can stop the deaths of innocent civilians."

Deputy Prime Minister Nick Clegg told a Whitehall press conference: "The very high levels of civilian deaths in Gaza, the humanitarian crisis, which is leaving thousands of people without water, without electricity, without medical assistance, without a home, is a form of collective suffering for the sins of Hamas, who are, unacceptably, firing rockets into Israel.

"I would, like everyone, urge restraint at this stage."