A number of children were among those who died when the al-Fakhura school in the Jabaliya refugee camp was hit, doctors at nearby hospitals said.
Earlier, the International Committee of the Red Cross (ICRC) warned of a "full-blown humanitarian crisis" in Gaza.
Speaking on Tuesday, a senior ICRC official, Pierre Kraehenbuhl, said life in Gaza had become intolerable.
Palestinian Health Ministry officials say 660 people have been killed since the attacks began, 195 of them children, BBC reported.
About 350 people had sought refuge at the school in an effort to escape the fighting.
The UN officials said they regularly provided the Israeli military with exact coordinates of their facilities, and that the school was in a built-up area.
UN Secretary-General Ban Ki-moon said he was "deeply dismayed" that despite these efforts, three UN-run schools had been hit by nearby Israeli strikes.
PA/PA
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MNA
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