Chris Gunness was overcome with emotion as he spoke on Al Jazeera Arabic.
He was speaking after the latest attack on a UN school which killed 19 people, and left over 100 injured.
The strike came hours after Israeli tank shells slammed into a UN school sheltering displaced Palestinians
The latest deadly strikes came on the heels of an escalation in the embattled coastal territory, with Israel and Gaza's Hamas rulers stepping up attacks after more than three weeks of fighting that has killed more than 1,300 Palestinians and more than 50 Israelis.
Witnesses said the shopping area was busy because residents, and many who had taken shelter in the area from fighting elsewhere, thought a ceasefire was in place.
The Israeli military had no immediate comment on the strike on the shopping area and said it was investigating the report.
Israel had earlier announced a "humanitarian window" in certain parts of the territory. But it said it would not halt fire in other areas, including in Shijaiyah, where the strike took place. Hamas dismissed the ceasefire, and Gaza militants fired 27 rockets at Israel after it began.