"The number of casualties has reached an unbearable point," Ban said at a meeting with Israeli Foreign Minister Tzipi Livni.
The UN chief's visit to Israel coincided with a large-scale military attack on Gaza City, which damaged a hospital and a UN office that coordinated efforts with Palestinian refugees. Three UN employees were injured and the office was destroyed by fire.
"I conveyed my strong protest and outrage to the defense minister and the foreign minister and demanded a full explanation," Ban said.
"The defense minister said to me it was a grave mistake," Ban said. "He assured me that extra attention will be paid to UN facilities and staff and this will not be repeated."
Over the 20 days of the Israeli military offensive in the Gaza Strip, more than 1,050 Palestinians have been killed, most of them civilians, according to the Palestinian health ministry. Israel has lost 13 people, nine of whom were military.
