The call from Rami Hamdallah came during a meeting with visiting UN Secretary-General Ban Ki-moon, who is in the region to shore up international efforts to rebuild Gaza.
In 50 days of fighting, more than 2,100 Palestinians were killed, most of them civilians, according to the United Nations.
An additional 11,000 people were wounded and some 100,000 people were left homeless. Seventy-two people on the Israeli side were killed, including 66 soldiers.
At a news conference with Ban in Jerusalem, Israeli Prime Minister Benjamin Netanyahu accused the UN of being complicit in rocket fire.
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"When rockets were discovered in UN schools, some UN officials handed them back to Hamas, that very same Hamas that was rocketing that very same time Israeli cities and Israeli civilians," Netanyahu said.
Ban did not address Netanyahu's accusations, but Pierre Krahenbuhl, the commissioner of the UN agency for Palestinian refugees, which runs the UN schools in Gaza, has "categorically" rejected the Israeli charges.
Israel and Egypt imposed the blockade after the Hamas takeover, largely restricting the movement of people and goods in and out of Gaza and stifling the local economy.