The statement issued through Ban's spokesperson said he had called for calm in talks with Israeli Prime Minister Ehud Olmert, Palestinian President Mahmoud Abbas, Egyptian President Hosni Mubarak, Syrian President Bashar Assad and other regional leaders.
He also spoke with members of the Quartet of Middle East peace negotiators - the European Union, United States, Russia and United Nations.
As of late Sunday at least 300 Palestinians had been killed in the fighting in the Gaza Strip. The statement said a UN relief worker and eight UN relief trainees were among the casualties.
The United Nations said Ban "deplores that violence is continuing today and he strongly urges once again an immediate stop to all acts of violence."
The UN Security Council earlier had called for an immediate end to all violence in Gaza. Ban underscored the council's call for Israel to open border crossings to Gaza to ensure its residents receive humanitarian supplies.
The UN's humanitarian coordinator in Gaza was told by Israeli officials that relief would be allowed in, the statement said.
On Sunday, Prime Minister Ehud Olmert spoke to German Chancellor Angela Merkel and explained Israel's considerations for launching the offensive in Gaza.
During their phone conversation Olmert told Merkel that Israel is targeting Hamas and the rest of the Palestinian terror groups, not the civilian population in Gaza.
Roni Sofer contributed to the report