At least 19 Palestinians were killed and about 90 injured early on Wednesday when a UN school sheltering displaced people was hit by shells during a second night of relentless bombardment that followed an Israeli warning of a protracted military campaign.

Pierre Krahenbuhl, commissioner-general of the UN agency for Palestinian refugees, UNRWA, condemned “in in the strongest possible terms this serious violation of international law by Israeli forces”.

He said in a statement: “Last night, children were killed as they slept next to their parents on the floor of a classroom in a UN-designated shelter in Gaza. Children killed in their sleep; this is an affront to all of us, a source of universal shame. Today the world stands disgraced.

“We have visited the site and gathered evidence. We have analysed fragments, examined craters and other damage. Our initial assessment is that it was Israeli artillery that hit our school, in which 3,300 people had sought refuge. We believe there were at least three impacts.

“It is too early to give a confirmed official death toll. But we know that there were multiple civilian deaths and injuries including of women and children and the UNRWA guard who was trying to protect the site. These are people who were instructed to leave their homes by the Israeli army.”

It was the sixth time that UNRWA schools had been struck, he added. “Our staff, the very people leading the humanitarian response are being killed. Our shelters are overflowing. Tens of thousands may soon be stranded in the streets of Gaza, without food, water and shelter if attacks on these areas continue.”

At the school, Assad Sabah said he and his five children were huddling under desks in one of the classrooms because of the constant sound of tank fire throughout the night.

“We were scared to death,” he told the Associated Press. “After 4.30am, tanks started firing more. Three explosions shook the school. One classroom collapsed over the head of the people who were inside.”

A spokeswoman from the Israel Defence Forces said that its initial inquiries showed that “Hamas militants fired mortar shells from the vicinity of the school, and [Israeli] soldiers responded by firing towards the origins of the fire”. An investigation was continuing, she added.

A UN source said there was no evidence of militant activity inside the school.

The shelling of the school came as diplomatic attention was focussed on Cairo, where a delegation including the Palestinian president, Mahmoud Abbas, and representatives of Hamas and Islamic Jihad, the main militant factions in Gaza, was due to take part in ceasefire talks. A key issue was whether the Gaza-based factions and their armed wings accepted the authority of the delegation.

The Israeli security cabinet was also due to meet on Wednesday afternoon and would consider any progress made in Cairo. Israel’s political and military leaders face crucial decisions on whether to press deeper into Gaza once the cross-border tunnels have been located and destroyed, or whether to accept a “quiet for quiet” deal. “The next 24-72 hours will be critical,” said a diplomatic source.

The last two nights have seen the most fierce bombardment in this Gaza offensive, with inense air strikes, tank shelling and bombardment from Israeli gunboats. In 23 days more than 1,240 Palestinians, most of them civilians, have been killed. On the Israeli side 53 soldiers and three civilians have been killed.

The shelling of the UN school followed an incident last week when another UN school in Beit Hanoun was hit as the playground was filled with families awaiting evacuation amid heavy fighting. Israel denied it was responsible for the deaths, saying a single “errant” shell fired by its forces hit the school playground, which was empty at the time.

But according to testimonies gathered by UN staff, an initial shell was followed by “several others in the close vicinity of the school within a matter of minutes”, spokesman Chris Gunness said. Reporters who visited the scene minutes afterwards said damage and debris was consistent with mortar rounds.

UNRWA, said on Tuesday it had found a cache of rockets at one of its schools in Gaza and deplored those who had put them there for placing civilians in harm’s way.

“This is yet another flagrant violation of the neutrality of our premises. We call on all the warring parties to respect the inviolability of UN property,” Gunness said. Two similar discoveries were made last week.

Israel says militants from Hamas and other organisations launch rockets from the vicinity of UNRWA properties.

More than 200,000 people in Gaza have taken shelter in the UN’s schools and properties after Israel warned them to leave whole neighbourhoods that it was planning to bomb. UNRWA said it was at “breaking point”.

The Israeli military said it had targeted more than 4,000 sites in Gaza since the start of the conflict on 8 July. It had detonated three tunnels in Gaza in the past 24 hours, it added. Among the overnight targets were five mosques, which the IDF said housed tunnel shafts, weapons stores and lookout posts, and two “facilities” utilised by senior Hamas militants.

International pressure for an end to the bloodshed has continued to mount. On Tuesday the British prime minister, David Cameron, added his weight to calls for an unconditional, immediate humanitarian ceasefire.

“What we’re seeing is absolutely heartbreaking in terms of the loss of life … everyone wants to see this stopped,” he said. Blaming Hamas for triggering the conflict, he added: “Hamas must stop attacking Israel with rocket attacks. That is how this started. It’s completely unjustified and they need to stop as part of the ceasefire.”

Four Latin American countries – Chile, Peru, Brazil and El Salvador – recalled their ambassadors to Israel. “Chile observes with great concern and discouragement that the military operations – which at this point appear to be a collective punishment to the Palestinian civil population in Gaza – don’t respect fundamental norms of international humanitarian law,” its foreign ministry said.

But support for the military operation among the Israeli public remained solid. A poll published by Tel Aviv university on Tuesday found 95% of Israeli Jews felt the offensive was justified. Only 4% believed too much force had been used.