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An Israeli bombardment hit outside a U.N. school where hundreds of Palestinians had sought refuge on Tuesday, and Palestinian medics said at least 34 people died — many of them children — as international outrage grew over civilian deaths.

It was the second fatal strike in the vicinity of a U.N. school in hours, and the deadliest assault since Israel sent ground forces into Gaza last weekend. The ground operation is part of a larger offensive against the ruling Hamas militant group that has killed nearly 600 Palestinians, including dozens of civilians, according to U.N. and Palestinian officials.

Ignoring international calls for a cease-fire, Israeli soldiers edged closer to Gaza’s major population centers. A total of 58 Palestinians were killed Tuesday in fighting — with just two confirmed as militants, health officials in Gaza said.

“There’s nowhere safe in Gaza. Everyone here is terrorized and traumatized,” John Ging, the top U.N. official in Gaza, said after the first strike on the compound of a U.N. school killed three people.

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

The United Nations said three civilians were killed in the first airstrike late Monday on the courtyard of its school, where hundreds of people from a Gaza City refugee camp had sought shelter from Israel’s blistering 11-day offensive.

A second Israeli strike about 10 yards (meters) outside a U.N. school in the northern Gaza town of Jebaliya. Witnesses reported several explosions, and it was not immediately clear whether they were caused by Israeli airstrikes or tank shells.

Dr. Bassam Abu Warda, director of Kamal Radwan Hospital, said 34 people were killed.

“I saw a lot of women and children wheeled in,” said Fares Ghanem, another hospital official. “A lot of the wounded were missing limbs and a lot of the dead were in pieces.”

Majed Hamdan, an AP photographer, said he rushed to the scene shortly after the attacks. He said many children were among the dead.

“I saw women and men — parents — slapping their faces in grief, screaming, some of them collapsed to the floor. They knew their children were dead,” he said. “In the morgue, most of the killed appeared to be children. In the hospital, there wasn’t enough space for the wounded.”

He said there were marks of five separate explosions, all in the same area outside the school.

U.N. officials say they provided their location coordinates to Israel’s army to ensure that their buildings in Gaza are not targeted.

The army declined comment, but said Hamas often uses schools, mosques and civilian areas for cover. Israeli government spokesman Mark Regev also refused to react, saying he was waiting for the military to comment.

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, including more than 100 civilians, according to United Nations and the latest Palestinian figures. Ten Israelis have died since the operation began, including a soldier who was shot on Tuesday.

“I am appealing to political leaders here and in the region and the world to get their act together and stop this,” Ging said, speaking at Gaza’s largest hospital. “They are responsible for these deaths.”

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

Tanks rumbled closer to the towns of Khan Younis and Dir el Balah in south and central Gaza but were still several kilometers (miles) outside, witnesses said, adding that the sounds of fighting could be heard from around the new Israeli positions. Israel already has encircled Gaza City, the area’s biggest city.

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.

“This is not a crisis, it’s a disaster,” said water utility official Munzir Shiblak. “We are not even able to respond to the cry of the people.” He said about 800,000 residents in Gaza City and northern parts of the territory had no access to running water from Tuesday.

Israel says it won’t stop the assault until its southern towns are freed of the threat of Palestinian rocket fire and it receives international guarantees that Hamas, a militant group backed by Iran and Syria, will not restock its weapons stockpile. It blames Hamas for the civilian casualties, saying the group intentionally seeks cover in crowded residential areas.

“The battle is bitter but unavoidable. We set out on this operation in order to deal Hamas a heavy blow and to alter living conditions in the south of the country and to block smuggling into the Gaza Strip,” Israeli Defense Minister Ehud Barak.

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. At least 15 rockets were fired Tuesday and one landed in the town of Gadera, about 25 miles (40 kilometers) from the Gaza border, lightly wounding a 3-month-old infant, police said. At the outset of the fighting, militants launched dozens of rockets each day.

Hamas is believed to have 20,000 fighters.

Israeli forces have seized the main Gaza highway in several places, cutting the strip into northern, southern and central sectors and preventing movement between them. Israel also has taken over high-rise buildings in Gaza City and destroyed dozens of smuggling tunnels — Hamas’ main lifeline — along the Egyptian border.

Late Monday, a paratroop officer and three Israeli infantrymen were killed in two separate friendly fire incidents, the military said. Heavy Israeli casualties could threaten to undermine what so far has been wide public support for the operation.

A high-level European Union delegation met with President Shimon Peres on Tuesday in a futile bid to end the violence. Commissioner Benita Ferraro-Waldner acknowledged Israel’s right to self-defense, but said its response was disproportionate.

“We have come to Israel in order to advance the initiative for a humanitarian cease-fire and I will tell you, Mr. President, that you have a serious problem with international advocacy, and that Israel’s image is being destroyed,” she said, according to a statement from Peres’ office.

In Geneva, the international Red Cross said Gaza was in a “full-blown” humanitarian crisis. Its head of operations, Pierre Kraehenbuehl, said the few remaining power supplies could collapse at any moment.

Israeli leaders say there is no humanitarian crisis and that they have allowed the delivery of vital supplies.

The EU delegation was one of a flurry of diplomatic efforts to forge a cease-fire. French President Nicolas Sarkozy left Israel after a day of meetings with leaders.

Europe “wants a cease-fire as quickly as possible,” Sarkozy said Monday, urging Israel to halt the offensive, while blaming Hamas for acting “irresponsibly and unpardonably.”

Prime Minister Ehud Olmert stressed to Sarkozy that any agreement “must contain at its foundation the total cessation of all arms transfers to Hamas,” said Israeli government spokesman Mark Regev.

Regev noted that Hamas used a previous six-month truce to double the range of its rockets. About one-eighth of Israel’s 7 million citizens now live in rocket range.

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.

He would not give details of an international proposal to stop the flow of weapons into Gaza from Egypt.

In New York, Arab delegates met with the U.N. Security Council, urging members to adopt a resolution calling for an immediate end to the attacks and a permanent cease-fire. Palestinian President Mahmoud Abbas, a Hamas rival who runs a separate government from the West Bank, was expected Tuesday morning to press his case.

Before Tuesday’s deaths, U.N. humanitarian chief John Holmes said the overall Palestinian toll since the opening of the Gaza campaign on Dec. 27 stood at about 500, with about 125 of them civilians.

Israeli forces detained 80 Palestinians — some of them suspected Hamas members — and transferred several to Israel for interrogation, said military officials, speaking on condition of anonymity because they were not allowed to release the information.

Israel’s operation has angered many across the Arab world and has drawn criticism from countries such as Turkey, Egypt and Jordan, which have ties with Israel and have been intimately involved in Mideast peacemaking.

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