Speaking at a campaign event in Phoenix, Arizona, Harris said Israel has the right to “go after Hamas” but also has a “significant responsibility” to avoid civilian casualties.
The Democratic presidential candidate also renewed his call for a ceasefire and a deal on the hostages.
Saturday’s airstrike was criticised by Western and regional powers, with Egypt saying it showed Israel had no desire to reach a ceasefire or end the war in Gaza.
Fadl Naeem, director of Al-Ahli Hospital, where many of the victims were taken, said that about 70 victims had been identified so far, while the remains of many of the victims were so disfigured that it was difficult to identify them.
The Israeli military said it “precisely struck Hamas terrorists operating inside a Hamas command and control center at the Taba’in School.”
“At least 19 Hamas and Islamic Jihad terrorists” were “eliminated” in the attack, the Israel Defense Forces and the Israeli Security Agency said in a statement.
Israeli military spokesman Admiral Daniel Hagari said “various intelligence indicators” indicated a “high probability” that the commander of the Islamic Jihad’s Central Camps Brigade, Ashraf Joudeh, was at the Taba’in school when it was bombed.
He said it was not yet clear whether the commander was killed in the attack.
Earlier estimates of the death toll had been in the dozens, with the Hamas-run Health Ministry’s ambulance service saying more than 60 people had been killed, according to the Associated Press. The civil defense agency said the toll had exceeded 90.
The BBC could not independently verify the figures from either side.
The Israeli spokesman said the casualty figures issued by Hamas officials “do not correspond to the information the IDF has, the precision munitions used, and the accuracy of the strike.”
Hamas described the attack as a “horrific crime and a dangerous escalation” in “Israel’s war of extermination against the Palestinian people.”
US National Security Council spokesman Sean Savitt said Hamas was using schools “as gathering sites and operating from.”
“But we have also said repeatedly that Israel must take the necessary measures to minimize harm to civilians,” he added.