Secretary Ban Ki-moon said Monday he deplores the deaths and calls UN locations "inviolable."
But the independent board of inquiry also found that Palestinian militant groups hid weapons at three empty UN schools in Gaza and that in two cases Palestinian militants "probably" fired from the schools. Ban called that "unacceptable."
The 2014 war was the most devastating for Gaza's 1.8 million people, killing more than 2,200 Palestinians, a majority of them civilians, according to UN figures. Seventy-two people were killed on the Israeli side, including 66 soldiers.
At a fourth girls' school, the inquiry said, "no prior warning had been given by the government of Israel of the firing of 155 MM high explosive projectiles on, or in the surrounding area of the school." At a co-ed college, one block was damaged by a projectile fired by an Israeli tank.
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The UN released its summary of the report but said the full 207-page report is private. The inquiry looked at 10 incidents.
Ban's statement stressed that the board of inquiry "does not make legal findings" and was not tasked with addressing the wider issues of the Gaza war.
In a statement, Israeli Foreign Ministry spokesman Emmanuel Nahshon said, "All of the incidents attributed by the report to Israel have already been subject to thorough examinations, and criminal investigations have been launched where relevant.
There was no immediate comment from the Palestinian mission to the UN.