The Palestinian Ministry of Health announced on Tuesday that at least 624 people have been killed and another 3750 since the start of the Israeli assault on the Gaza Strip.

 

In the latest attacks, Israeli strikes killed at least 13 women and children in Gaza, medics said, as the army announced the deaths of two more soldiers in the two-week conflict.

 

The fatalities, which were among nearly 40 on Tuesday alone, brought the total death toll to more than 600 Palestinians, according to Gaza's emergency services, and 29 Israelis -- 27 soldiers and two civilians.

 

A child and three women, one of them pregnant, were killed in two separate Israeli air strikes in Zeitun, in the central Gaza Strip, and Beit Hanun, in the north, emergency services spokesman Ashraf al-Qudra said.

 

An elderly woman and her brother were among those killed in three separate raids targeting Bureij and Al-Maghazi in central Gaza, and Rafah in the south.

 

And a series of Israeli air strikes early Tuesday killed seven people.

 

Tuesday's toll included 10 women and three children, according to Qudra.

 

Also on Tuesday, a United Nations school sheltering displaced Palestinians in central Gaza came under Israeli fire as a team was inspecting damage from a day earlier, a U.N. official said.

 

The official said a team, with Israeli clearance, was at the school run by the U.N. agency for Palestinian refugees UNRWA in Al-Maghazi when Israeli tank shelling resumed, hitting the building on Tuesday afternoon.

 

"Yesterday we got reports that it was shelled and so today we sent our guys down to investigate and see which side the fire came from," the official said, speaking to Agence France Presse on condition of anonymity.

 

"They went down there with Israeli clearance, and while they were there, they came under Israeli shelling," he added.

 

He said that there were holes blown through the walls of the school compound and that the gates had been blown off but no one was injured in the shelling.

 

The school has been evacuated and UNRWA has submitted a formal letter about the shelling to Israel, he added.

 

UNRWA is sheltering more than 100,000 people at more than 60 of its schools throughout the Gaza Strip.

 

Many Palestinians living in border areas of Gaza have been warned by Israel to flee their homes, but they say they feel nowhere in the coastal enclave is safe for them.

 

On Thursday, UNRWA said it was investigating after finding 20 rockets hidden in one of its vacant schools.

 

It condemned the incident as a "flagrant violation" of international law and said the rockets had been removed and the "relative parties" informed.

 

It said the incident was the first of its kind.

 

The Israeli army, meanwhile, confirmed that a soldier, who Hamas militants claimed they had kidnapped, was dead and his body remains unaccounted for.

 

The army named the soldier, whose body is still missing, as Oron Shaul, two days after Hamas said they had kidnapped an Israeli soldier of the same name.

 

The Israeli military said two more of its soldiers had been killed in the fighting a day earlier, hiking the overall Israeli death toll to 29, among them 27 soldiers who died in the past four days.

 

Tuesday's bloodshed pushed the total Palestinian toll to over 600 since the Israeli military launched Operation Protective Edge on July 8 in a bid to stamp out rocket fire from Gaza.

 

Two Israeli civilians have been killed since July 8 by cross-border rocket fire.

 

Meanwhile, the U.N. chief and Washington's top diplomat were holding a flurry of meetings in Cairo on Tuesday to push for an end to violence in Gaza.

 

As the conflict entered its third week, neither side showed any sign of willingness to pull back, with Israel pursuing a relentless campaign of shelling and air strikes, and militants hitting back with rocket fire and fierce attacks on troops operating on the ground.

 

Israeli Justice Minister Tzipi Livni said Israel will not halt its fire in Gaza until it finishes an operation aimed at destroying tunnels used by militants for cross-border attacks.

 

As world efforts to broker a ceasefire in war-torn Gaza gathered pace, Livni also ruled out any acceptance of the "unacceptable" demands laid out by Hamas as a condition for halting its fire.

 

She said the question of an immediate ceasefire with Hamas was not going to happen at this stage.

 

"First of all, it won't happen before we really finish the tunnels project which was laid out as a strategic objective," she told Ynet news website, referring to a major operation that started on the evening of July 17.

 

"Second, it won't happen in a way in which Hamas's completely unacceptable conditions are met, because it just wont," she said.

 

"Until now, Hamas is presenting demands that have no chance of being accepted by anyone -- not by us, not by Abu Mazen, not by the Egyptians and not by the Americans," she said, referring to Palestinian president Mahmud Abbas.

 

"In a situation where Hamas says 'Give us everything or the fighting will continue,' well then the fighting will continue," she said.

 

Last week, an Egyptian ceasefire proposal was accepted by Israel but rejected by Hamas, which kept up its rocket fire across the border. After five hours of holding fire, Israel resumed its punishing operation in Gaza.

 

Hamas officials have laid out a list of demands that must be met before agreeing to a truce -- some involving Israel and others aimed at Egypt.

 

Central to its demands is that Israel lift its eight-year blockade on Gaza and release of scores of veteran Palestinian prisoners who had been released in a 2011 swap agreement but who were recently re-arrested.

 

It also wants the Rafah border crossing with Egypt to be opened, in a demand aimed at Cairo which has kept it largely closed since the overthrow in July 2013 of former Islamist president Mohammed Morsi, a key Hamas ally.

 

A majority of Israelis support continuing the operation, a survey conducted by daily freesheet Israel Hayom said.

 

Some 77 percent of respondents opposed an immediate ceasefire, with only 16 percent supporting it, the poll said, and a vast majority (94 percent) said they were satisfied with the way the army was carrying out the campaign.

 

The poll interviewed 500 Jewish Hebrew-speaking Israeli adults.

 

World powers have urged Hamas to accept the Egyptian-brokered ceasefire and stop raining rockets into Israel from the Gaza Strip, demands it has so far resisted.

 

U.S. Secretary of State John Kerry again placed the onus on Hamas to accept a ceasefire along the lines of the Egyptian proposal to end the conflict raging in Gaza.

 

The top U.S. diplomat was speaking in Cairo after meeting Egyptian President Abdel Fattah al-Sisi.

 

Kerry voiced support for the initiative as a "framework" to end violence.

 

And U.N. chief Ban Ki-moon demanded that Israel and Hamas halt the spiraling violence in Gaza as he pushed diplomatic efforts to end bloodshed.

 

Following top-level truce talks in Cairo, the U.N. secretary-general headed to Israel to deliver his message in person as the 15-day conflict showed no sign of easing.

 

"My message to Israelis and Palestinians is the same: Stop fighting, start talking and take on the root causes of the conflict so that we are not at the same situation in the next six months or a year," he said.