GAZA CITY, Gaza — An Israeli bombardment struck outside a UN school where hundreds of Palestinians had sought refuge on Tuesday, the U.S. and Palestinian medics said, killing at least 30 people — many of them children whose parents wailed in grief at a hospital filled with dead and wounded.

An Israeli official said its soldiers came under fire from militants hiding in the school and that the building stored Palestinian munitions.

Despite international criticism over civilian deaths and calls for a ceasefire, Israeli soldiers edged closer to two major Gaza towns. A total of 58 Palestinians were killed Tuesday — with just two confirmed as militants, health officials in Gaza said.

The explosions marked the second time in hours a U.S. school came under attack. It was the deadliest assault since Israel sent ground forces into Gaza last weekend as part of a larger offensive against the ruling Hamas militant group that has killed nearly 600 Palestinians.

Nearly half of the dead are civilians, according to U.S. and Palestinian officials.

“There’s nowhere safe in Gaza. Everyone here is terrorized and traumatized,” John Ging, the top U.S. official in Gaza, said after the first strike on the compound of a U.S. school killed three people in a courtyard. The school has served as a shelter for Gaza City refugees fleeing the blistering 11-day offensive.

A Palestinian rocket — one of two dozen fired from Gaza on Tuesday — wounded an Israeli infant.

Dr. Bassam Abu Warda, director of Kamal Radwan Hospital, said 34 people were killed in an Israeli strike outside a second U.S. school in the northern Gaza town of Jebaliya. The United Nations confirmed 30 were killed and 55 injured by tank shells.

But an Israeli official said “hostile fire” was directed at the soldiers from within the school. He said soldiers returned fire and multiple explosions went off, presumably emanating from munitions stored there. The official spoke on condition of anonymity pending a formal army announcement.

The attack occurred at mid-afternoon, at a time when many people in the densely populated Jebaliya refugee camp were out and about. Many of the refugees apparently had stepped outside the shelter to get some air, thinking an area around a school was safe.

Palestinian militants frequently fire from residential areas. However, Mohammed Nassar, a medic who treated the wounded, said he did not see any gunmen among the casualties.

Footage broadcast on Hamas’ Al Aqsa TV showed gruesome scenes at the hospital. At first, medics carried in at least five younger boys who were laid out on the hospital floor. It was not clear whether they were still alive.

Other medics then started unloading bodies of older men who had been stacked up in the back of an ambulance, three high, and were dragged without stretchers. One man’s legs had been turned into bloody stumps that dragged on the ground as he was pulled from the ambulance.

U.S. officials say they provided their location co-ordinates to Israel’s army to ensure that their buildings in Gaza are not targeted.

Speaking shortly after the first attack, Maxwell Gaylard, the U.S. humanitarian co-ordinator for the Palestinian territories, demanded an investigation.

“As one of the most densely populated places in the world, it is clear that more civilians will be killed,” he said. “These tragic incidents need to be investigated, and if international humanitarian law has been contravened, those responsible must held accountable.”

The international Red Cross said an ambulance post was hit as well on Tuesday, injuring one medical worker.

Israel launched its offensive on Dec. 27 to halt repeated Palestinian rocket attacks on its southern towns. After a weeklong air campaign, Israeli ground forces invaded Gaza over the weekend.

Nearly 600 Palestinians have been killed. Ten Israelis have died since the operation began, including a soldier who was shot on Tuesday.

United Nations staff estimate around 15,000 people have fled to 23 U.S.-run schools they have turned into makeshift refuges. U.S. food aid has halted in the northern Gaza Strip because officials fear residents would risk their lives to reach distribution centres.

The rising civilian death toll has drawn international condemnations and raised concerns of a looming humanitarian disaster. Many Gazans are without electricity or running water, thousands have been displaced from their homes and residents say that without distribution disrupted, food supplies are running thin.

Visiting southern Israel, Prime Minister Ehud Olmert said he hoped to stop the offensive soon, but said it would depend on Hamas’ willingness to stop attacks and stop its smuggling of weapons into Gaza from neighbouring Egypt.

“We have no interest in endlessly continuing the campaign. It will stop when the conditions that are essential for Israel’s security are met,” he said in the rocket-scarred town of Sderot.

The army says it has dealt a harsh blow to Hamas, killing 130 militants in the past two days and greatly reducing the rocket fire. Hamas is believed to have 20,000 fighters.

International Mideast envoy Tony Blair said ensuring weapons smuggling to Hamas is halted would be a key step to restoring calm.

Speaking to reporters in Jerusalem, Blair said that stopping Hamas’ rocket supply would be a “very significant advance in terms of Israel’s security,” which would allow Israel to halt its offensive and relieve the suffering of Gaza’s civilians.