The civilian death toll in Gaza increased dramatically today, with at least 12 members of an extended family, including seven young children, killed in an air strike on their house in Gaza City while the bombing of two United Nations schools being used as shelters took 13 lives.

The bodies of the Daya family were pulled from the rubble of a house in Gaza City's Zeitoun area after it was hit by two Israeli missiles. The dead included seven children aged from one to 12 years, three women and two men. Nine other people were believed to be trapped in the rubble.

Israeli missiles also struck a UN school in Jabaliya refugee camp, which was being used as a shelter by people forced from their homes by the fighting, according to news agency reports. Ten of the refugees were killed.

Hours earlier, three young men – all cousins – died when Israeli forces bombed Asma elementary school in Gaza City. They were among about 400 people who sought shelter there after fleeing their homes in Beit Lahia, in northern Gaza.

The UN, which said the school was clearly marked, said it was "strongly protesting these killings to the Israeli authorities and is calling for an immediate and impartial investigation".

"Where it is found that international humanitarian law has been violated, those responsible must be held to account. Under international law, installations such as schools, health centres and UN facilities should be protected from attack. Well before the current fighting, the UN had given to the Israeli authorities the GPS coordinates of all its installations in Gaza, including Asma elementary school."

The killings take the total toll in Palestinian lives since the Israelis launched their assault on the Gaza strip 11 days ago to more than 600. Doctors at Gaza hospitals say that at least one-fifth of the victims are children and that a large number of women are among the dead.

Israel continues to insist that the bulk of those killed are Hamas and Islamic Jihad fighters, although its claim to be going to extraordinary lengths to target only "terrorists" has been undermined by one of its own tanks firing on a building being used by Israeli troops, killing four.

The sharp spike in the number of civilian casualties came as Israeli troops and tanks moved into Gaza's second largest city, Khan Younis, for the first time today supported by intensive artillery strikes as the military pledged to press on with its attack.

The heaviest fighting has been in northern Gaza, with witnesses reporting wave after wave of bombing strikes across the north of the territory accompanied by gunfire from helicopters and artillery from land and sea. Thousands of Palestinians have been ordered to leave their homes or forced to flee the fighting.

In Shajaiyeh, east of Gaza City, Israeli troops seized control of three apartment blocks and set up gun positions on the rooftops. Residents were locked in their homes and soldiers confiscated their mobile phones, neighbours said.

Three of the four Israeli soldiers killed by friendly fire died when a tank mistakenly fired on a building where the soldiers had taken up positions. There was heavy artillery fire to cover the evacuation of 24 soldiers who were injured, including the commander of the Golani infantry brigade, one of Israel's key fighting forces.

Israel's defence minister, Ehud Barak, said his country's troops would continue their operation despite mounting Palestinian casualties and growing international calls for a ceasefire.

"Hamas has so far sustained a very heavy blow from us, but we have yet to achieve our objective, and therefore the operation continues," Barak said.
The Israeli foreign minister, Tzipi Livni, said the offensive was intended to change permanently the shape of Israel's conflict with Hamas. "When Israel is targeted, Israel is going to retaliate," she said. Israel has rejected calls for a ceasefire.

The military said it had bombed more smuggling tunnels across the border with Egypt, in the south, and hit more than 40 other sites across Gaza including buildings storing weapons and rocket launching areas.

In Gaza, Mahmoud Zahar, the most senior leader of Hamas in the strip and a hardliner in the movement, appeared on the party's al-Aqsa television station and gave a defiant speech threatening attacks not only in Gaza but elsewhere.

"The Zionists have legitimised the killing of their children by killing our children. They have legitimised the killing of their people all over the world by killing our people," Zahar said. He urged Hamas fighters to "crush your enemy".

Another Hamas figure, a recognised military spokesman called Abu Ubaida, said thousands of Hamas fighters were waiting in Gaza to take on the Israeli military, and that rocket attacks would increase. More than 40 were fired into southern Israel yesterday, including one that landed in an empty kindergarten, which, like all schools near the Gaza border, has been closed since the conflict began.. Israeli police said a total of 520 rockets had been fired in the past 11 days of fighting.

Israeli troops are now deployed in and around the major urban areas of Gaza, particularly to the north, in Beit Hanoun, Beit Lahiya and Jabaliya. Using leaflets, telephone calls and radio announcements, they have ordered residents in many areas to leave their homes, forcing at least 15,000 Palestinians to flee to safety elsewhere. At least 5,000 are staying in 11 different UN schools and shelters.

The UN said more than 1 million Gazans were still without electricity or water and that it was increasingly difficult for staff to distribute aid or reach the injured. It said more industrial diesel was needed to reopen the strip's sole power plant, which has been shut for a week. Ten transformers have been damaged in the fighting.

More wheat grain is needed for food handouts, and the UN said Karni, the main commercial crossing, should be reopened to allow it in. Four ambulances and three mobile clinics were destroyed when bombs hit the headquarters of the Union of Health Care Committees in Gaza City.

John Holmes, the UN emergency relief coordinator, said Gaza represented an "increasingly alarming" humanitarian crisis, and that the territory was running low on clean water, power, food, medicine and other supplies since Israel began its offensive. Israeli leaders claim there is no humanitarian crisis.