The UN Security Council is set to resume debate on a ceasefire call in New York, with Palestinian Authority President Mahmoud Abbas, several Arab foreign ministers, UK Foreign Secretary David Miliband and US Secretary of State Condoleezza Rice among those attending.
At least 125 Palestinians and five Israeli soldiers were killed on Tuesday.
One soldier was killed in an exchange of fire with militants in Gaza City, while four others were killed by shellfire from their own tanks earlier in the day, Israeli military officials said.
Israel says its offensive is stopping militants firing rockets, but at least five hit southern Israel on Tuesday, with one reaching the town of Gedera, about 40km (25 miles) from Gaza, and injuring a baby.
Four Israeli civilians have been killed by rocket fire from the Gaza Strip since the offensive began.
In other developments:
Israeli forces push further south in the Gaza Strip and clash with militants near Gaza City
Skirmishes are reported on the edges of the Deir al-Balah and Bureij refugee camps in central Gaza
Witnesses say Israeli tanks and soldiers are advancing on the southern town of Khan Younis
Venezuela orders the expulsion of Israel's ambassador in protest at the offensive and its "flagrant violations of international law"
Many claims cannot be verified. Israel is refusing to let international journalists into Gaza, despite a Supreme Court ruling to allow a limited number of reporters to enter the territory.
The UN aid agency in Gaza, Unrwa, said three artillery shells had landed close to the al-Fakhura school on Tuesday afternoon, spraying shrapnel on people both inside and outside the building.
About 350 people had sought refuge at the school in an effort to escape the fighting between Israeli soldiers and militants on the outskirts of the Jabaliya refugee camp, to the east of Gaza City.
Television footage showed bodies scattered on the ground amid pools of blood.
The UN officials said they regularly provided the Israeli military with exact co-ordinates of their facilities, and that the school was in a built-up area.
UN Secretary-General Ban Ki-moon said he was "deeply dismayed" that despite these efforts, three UN-run schools had been hit by nearby Israeli strikes.
The Israeli military said that, according to initial checks, its soldiers had come under mortar fire from militants inside the al-Fakhura school.
"The force responded with mortars at the source of fire," it said in a statement. "Hamas cynically uses civilians as human shields."
It later reported that two well-known members of a Hamas rocket-launching cell had been among those killed at the school, naming them as Imad and Hassan Abu Askar.
Israeli government spokesman Mark Regev said the incident was a "very extreme example of how Hamas operates".
"If you take over - I presume with guns - a UN facility. If you hold the people there as hostages, you shoot out of that facility at Israeli soldiers in the neighbourhood, then you receive incoming fire - I think that's a war crime under international law," he told the BBC.
A Hamas spokesman, Fauzi Barhoun, said allegations that fighters had used the school to attack Israeli forces were "baseless".
"There was no fire of any kind from the school," he told the BBC.
Two unnamed residents who spoke to an Associated Press reporter by phone said a group of militants had been firing mortar shells from near the school.
Earlier in the day, at least three Palestinians were killed when another school was hit in the Shati camp, UN officials said.
The BBC's Rushdi Abu Alouf reports from a UN school inside a Gaza refugee camp
Ten people were also injured at a UN health centre in the Bureij refugee camp.
Maxwell Gaylard, the UN humanitarian co-ordinator for the Palestinian territories, described the incidents as tragic and demanded an independent investigation.
The director of operations for Unrwa, John Ging, told the BBC that conditions in Gaza were "horrific" and that nowhere was safe for civilians there.
Mr Ging said international leaders had a responsibility to act to protect civilians, some 14,000 of whom are sheltering in UN buildings.
Diplomatic efforts to try to end the violence are gathering pace.
French President Nicolas Sarkozy said he had asked his Syrian counterpart, Bashar Assad, to help convince Hamas to co-operate with efforts to end the Israeli offensive. Syria is regarded as a main backer of Hamas.
The loss of civilian life in Gaza and Israel is a source of deep concern for me
US President-elect Barack Obama
Asked about the deaths at the UN school in Gaza, Mr Sarkozy said: "It reinforces my determination for all this to stop as quickly as possible."
He later held talks with Egyptian President Hosni Mubarak in Sharm el-Sheikh, who offered to hold talks with Israel and the Palestinians on border security without delay.
US state department spokesman Sean McCormack said the US would like to see "an immediate ceasefire" in Gaza.
US President-elect Barack Obama, meanwhile, broke his silence about the conflict, telling reporters that "the loss of civilian life in Gaza and Israel is a source of deep concern for me".
However, he also reiterated his principle that only President George W Bush would speak for US foreign policy at this time.
The BBC's Laura Trevelyan in New York says the contours of an agreement are taking shape - international monitors along the Egypt-Gaza border to stop Hamas smuggling weapons and firing rockets at Israel, and the creation of a humanitarian corridor in southern Gaza to ensure that aid reaches the Palestinians.
The question now is whether Hamas will accept such a deal and if a call for a ceasefire will be heeded by Israel, our correspondent says.
Hamas has said that Israeli attacks on Gaza must stop and the crossings into the territory, which Israel controls, must be fully opened, before it agrees to a ceasefire.
Israeli Prime Miniser Ehud Olmert said on Tuesday that the military campaign in Gaza would continue until Israel had completely wiped out Hamas's ability to fire rockets into Israel.
Update: In February 2009, the United Nations said that a clerical error had led it to report that Israeli mortars had struck a UN-run school in Jabaliya, Gaza, on 6 January killing about 40 people. Maxwell Gaylord, the UN humanitarian co-ordinator in Jerusalem, said that the Israeli Defense Force mortars fell in the street near the compound, and not on the compound itself. He said that the UN "would like to clarify that the shelling and all of the fatalities took place outside and not inside the school".
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