The Israeli offensive has so far killed 978 Palestinians while Israel says 10 soldiers and three civilians have died.
Michele Montas, a UN spokeswoman, said Ban would also "demand that urgent humanitarian assistance be provided without restriction to those in need".
"Everybody supported the role that the secretary-general can play. The security council is united ... We think the timing is right," Jean-Maurice Ripert, the French ambassador to the security council, said.
Diplomats said they also expected Ban to discuss with regional leaders reconstruction in Gaza after the violence ends, an effort the United Nations is expected to lead.
The UN chief said that he would send an assessment team to determine the extent of the damage and of humanitarian needs following a ceasefire.