The Israeli offensive has so far killed 984 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.
The diplomatic push by the UN chief to end the war came as the president of the UN General Assembly condemned the Israeli assault as "genocide".
"The number of victims in Gaza is increasing by the day... The situation is untenable. It's genocide," Miguel d'Escoto Brockmann told Al Jazeera at the UN in New York.
Miguel Moratinos, Spain's foreign minister, meanwhile met Mubarak as diplomatic efforts to end the Gaza conflict gathered pace.
Moratinos is one of several high profile officials touring the region to secure a ceasfire deal.
Qatar has also asked the 22-member Arab League to hold an emergency Arab summit in Doha, the Qatari capital, on Friday. A separate economic summit will be held in Kuwait on Sunday.
Diplomats said that Egypt and Saudi Arabia, both key allies of the US, have been cool to the idea of a summit because it could produce little in the way of results and thus make Arab leaders appear ineffective.
However, a statement released by the Saudi Press Agency, said that both Saudi Arabia and Egypt would take part in the emergency summit, but their presence at the emergency summit has not been confirmed.