According to a statement issued by his spokesperson, Ban said that it is in the interest of both sides that "steps toward dangerous escalation be replaced with immediate measures" to end the fighting, thus preventing further casualties and greater risks to regional peace and security.
Ban demanded both sides "move in this direction now," noting that he did not believe the dispute between Israelis and Palestinians can be resolved by either side via military means.
Ban's call was echoed by the UN Children's Fund (UNICEF), which urged all sides to urgently exercise maximum restraint, Xinhua reported.
"No child should have to suffer the terrifying impact of such violence," said UNICEF Executive Director Anthony Lake on Sunday in a statement.
Lake warned that children who witnessed such violence too often, and came to view it as "normal," were likely to repeat it themselves in later life. UNICEF figures showed that at least 33 children have been killed in Gaza in recent days, and hundreds more injured.