"Israel must do more to meet its own standards and avoid civilian casualties," US State Department spokeswoman Jen Psaki said.
Israel's military, hours after the attack, confirmed it had targeted three Islamic Jihad militants on a motorbike "in vicinity of an UNRWA school in Rafah. The IDF is reviewing the consequences of this strike."
And its Prime Minister Benjamin Netanyahu issued a statement early Monday saying that contrary to Gaza's de facto Islamist rulers Hamas, who have targeted Israeli citizens with thousands of rockets they have fired at the Jewish state over the past weeks, Israel attempts to refrain from killing uninvolved Palestinians.
"Israel does not aim its fire at civilians and is sorry for any attack that unintentionally hits civilians," he said without directly addressing the attack on the school.
UN Secretary General Ban Ki-moon called the attack "a moral outrage and a criminal act".
"This madness must stop," he said.
The strike came as Palestinian factions gathered for truce talks with Egypt in Cairo and world powers voiced increasingly urgent calls for both sides to cease fire.
"The bloodshed needs to stop," said a statement signed by the European Union and the European Commission presidents on behalf of the bloc's 28 members.
"We deplore the terrible loss of lives, including innocent women and children," it said, condemning the "intolerable violence" in Gaza as Israel presses its assault aimed at halting Hamas rocket fire.
French President Francois Hollande said the bombing of the school was "unacceptable", backing calls by Ban "to ask that those responsible for this violation of international law answer for their actions", without saying who he considered responsible.
But there was little respite on the ground, where more than 71 people were killed in Rafah alone as more bloodshed sent the death toll soaring over 1,800.
In Israel, 108 rockets and mortars fired from Gaza struck throughout the country Sunday, a military spokeswoman said, with another eight rockets intercepted by the Iron Dome defence system.
- Hospitals in crisis -
At the school, an AFP correspondent witnessed scenes of chaos as adults sprinted frantically away through pools of blood, young children clutched in their arms.
With hospitals and clinics under increasing pressure, Gaza's medical services have reached the brink of collapse, the UN warned.
Rafah's main Najjar hospital is closed after being hit and only two clinics were functioning, with medics rapidly running out of space.
In one, an AFP correspondent saw the bodies of four small children packed into an ice cream freezer.
Also Sunday, an Israeli air strike on northern Gaza killed at least seven people and wounded 15, the Palestinian health ministry said.
Intensive international attempts to broker a diplomatic end to the fighting have so far proved fruitless, but efforts are continuing with a Palestinian delegation in Cairo for talks with US and Egyptian officials.
Israel's security cabinet decided not to send a representative.
The Palestinians, who met Sunday to hammer out a common position, want "a ceasefire; Israeli troop withdrawal from Gaza; the end of the siege of Gaza and opening of its border crossings," said Maher al-Taher, a member of the delegation.
- Unilateral withdrawal? -
In the Monday statement, Netanyahu said the Gaza operation "will continue until its goals are reached: a return of quiet and security for Israeli citizens for a long period, while significantly harming terror infrastructure."
"After completing our actions against the terror tunnels aimed at a mass attack against Israeli civilians, the IDF (Israel Defence Forces) will deploy for further activity according to our security needs, until our goals are achieved," he said, echoing a Saturday remark seen as being the harbinger of a unilateral Israeli withdrawal.
On Sunday, the army confirmed it had begun withdrawing some troops from Gaza.
"We are removing some (forces)," Lieutenant Colonel Peter Lerner told AFP, saying troops were "extremely close" to completing a mission to destroy a network of tunnels.
"We are redeploying within the Gaza Strip, taking out other positions," he said, indicating that the military was "changing gear".
Witnesses had on Saturday reported seeing troops leave Beit Lahiya and Al-Atatra in the north as well as from villages east of Khan Yunis in the south.
On Sunday, AFP correspondents reported around 100 tanks gathering in the border area outside Gaza where they had not been before, having just pulled out, while others were seen driving away from the border.