International scrutiny of Israel's assault on the Gaza Strip intensified on Thursday when more than 15 Palestinians were killed and 200 injured in a strike on a UN school in northern Gaza crowded with hundreds of displaced civilians.

Most of the injured were women and children. Among the dead was a mother and her one-year-old baby. UN staff had been attempting to organise the school's evacuation when the attack took place.

Ban Ki-moon, secretary general of the UN, condemned the attack, which came hours after the agency had warned that Israel's actions in the Palestinian enclave could constitute war crimes. "Today's attack underscores the imperative for the killing to stop and to stop now," Ban said.

The Israeli military first claimed, in a text sent to journalists, that the school could have been hit by Hamas missiles that fell short. Later, a series of tweets from the Israel Defence Forces appeared to confirm the deaths were the result of an Israeli strike.

"Today Hamas continued firing from Beit Hanoun. The IDF responded by targeting the source of the fire."

"Last night, we told Red Cross to evacuate civilians from UNRWA's shelter in Beit Hanoun btw 10am & 2pm. UNRWA & Red Cross got the message. Hamas prevented civilians from evacuating the area during the window that we gave them."

The attack was condemned by Ban Ki-Moon, who said 'Today's attack underscores the imperative for the killing to stop and to stop now.' Photograph: Nidal Alwaheidi/Demotix/Corbis

Chris Gunness, spokesman for the United Nations Relief and Works agency said there had earlier been "firing around the compound" and his organisation had asked the Israeli army for time to evacuate civilians. "We spent much of the day trying to negotiate or to coordinate a window so that civilians, including our staff, could leave. That was never granted … and the consequences of that appear to be tragic." Gunness said the Israeli military were supplied with coordinates of UN schools where those displaced were sheltering. UN sources told the Guardian a call was placed to the Israeli military at 10.55am requesting permission to evacuate but their call was not returned.

The deaths in Beit Hanoun raised the overall Palestinian death toll in the conflict that began on 8 July to at least 751. Israel has lost 32 soldiers – all since 17 July, when it widened its air campaign into a full-scale ground operation – and three civilians.

The majority of those injured in the attack on the school were women and children. Photograph: Lefteris Pitarakis/AP

Hours after the attack, a trail of bloody footprints could be seen crossing a deserted playground littered with abandoned possessions. There were pools of blood both inside and outside the school building; more blood splashed over wooden school desks.

The Israeli military, which said it was "reviewing the incident", claimed the incident had occurred during "heavy combat" in the area and accused "terrorists" of "using civilian infrastructure and international symbols as human shields".

Although missiles belonging to Hamas and other armed Palestinian groups in Gaza do sometimes fall short, there was no visible evidence of debris from broken Palestinian rockets in the school. The injuries and the number of fatalities were consistent with a powerful explosion that sent shrapnel tearing through the air, in some cases causing traumatic amputations.

The surrounding neighbourhood bore evidence of multiple Israeli attacks, including smoke from numerous artillery rounds and air strikes. One building was entirely engulfed by flames.

The attack happened as the playground was crowded with families waiting to be ferried to safety. Photograph: Adel Hana/AP

Thursday's assault on the school – one of the grimmest incidents of the war – occurred at about 2.50pm as the playground was crowded with families waiting to be ferried to safety. According to survivors, one shell landed in the schoolyard followed by several more rounds that hit the upper stories of the building.

Most of the wounded were moved initially to a local hospital where terrified women and children clung to each other, waiting for news of relatives. A shell exploded about 50 metres from the hospital building as they waited.

Nour Hamid, 17, was hoping for news of her sister. As she attempted to comfort her terrified nephew, she said: "We were packing up to leave when the attack happened. We were standing outside when they started hitting us, some of the women holding their babies. My sister-in-law was one of the injured. There were bodies everywhere, most of them women and children."

Laila al-Shinbari told Reuters: "All of us sat in one place when suddenly four shells landed on our heads … Bodies were on the ground, [there was] blood and screams. My son is dead and all my relatives are wounded including my other kids."

Sabah Kafarna, 35, had also been sheltering at the school. "At about 11.30 someone from the municipality came to tell us that we were going to be moved because it was too dangerous. But the buses didn't come. That's why [there were] so many people all outside when the shells landed," she said. "The shells came one after the other. I was inside by the windows when they smashed."

Ayman Hamdan, medical director at Beit Hanoun hospital, told the Guardian that medical staff were treating multiple shrapnel injuries and damage to internal organs. "Some of the bodies were blown apart. Such a massacre requires more than one hospital to deal with it," she said.

The playground of the school, filled with displaced families when the shell hit. Photograph: Sameh Rahmi/NurPhoto/Corbis

The dead were ferried along with the most seriously injured in a fleet of ambulances to the relative safety of the Kamal Adwan hospital in Beit Lahia. Frantic relatives crowded the morgue looking for loved ones. The hospital's emergency room was plunged into chaos as doctors struggled to cope with the influx.

One father, his white singlet stained with blood, sat on the floor cradling the body of his injured daughter as another relative held a drip above her. Two more children were brought in – one girl injured by shrapnel, and another body whose torso was covered in blood.

Several UN schools have come under fire in the last week. On Tuesday, a school in Maghazi, central Gaza, sheltering about 1,000 people, was hit by Israeli shells as an UNRWA team inspected damage caused by an earlier strike. Thursday's strike occurred during a day of heavy fighting across the territory as Israel pressed ahead with its operation to halt rocket fire from Gaza and destroy a sophisticated network of cross-border tunnels.