The call came in a meeting between Foreign Minister Sheikh Sabah Khaled Al-Sabah and Ban who arrived in Kuwait on Monday in the second leg of a regional tour aimed at pushing for a ceasefire in Gaza.
The foreign minister "renewed Kuwait's support for the Palestinian people and condemned all Israeli acts of aggression," the official KUNA news agency reported following the meeting.
"He called on the UN Secretary General to urge the international community to shoulder responsibility to put an end to this dangerous aggression," it said.
Ban condemned the "atrocious action" of Israel's attack on Shejaiya, near Gaza City, where a blistering assault that started at dawn killed 62 people and wounded at least 250.
According to figures provided by Palestinian emergency services, the total number of Gazans killed since the beginning of the Israeli military aggression against Gaza on July 8 stands at 504. More than 3,000 people have also been injured in the attacks.
RA/NJF