But the Jewish state has also signalled a readiness to expand the operation.
All the signs point to preparations for a ground operation, with the army sealing all roads around Gaza and some 40,000 reservists reportedly massed along the border.
The latest negotiations aimed at ending the conflict, conducted behind closed doors in Cairo, ended without agreement. But all sides have expressed a willingness to engage in more talks.
The UN chief flew to Egypt “to add his diplomatic weight to these efforts, which are considerable and extremely important”, his spokesman Martin Nesirky said.
As Russia accused the United States of seeking to “filibuster” a UN Security Council statement on Gaza, Ban was to meet Egypt’s Foreign Minister Mohammed Kamel Amr, and President Mohamed Morsi and Arab League chief Nabil al-Arabi on Tuesday, Nesirky said.
He will then go to Jerusalem to see Israeli leaders but has no plan to go to Gaza.
The League’s Arabi is due in Gaza on Tuesday, accompanied by Turkish Foreign Minister Ahmet Davutoglu and several Arab top diplomats, in the latest in a series of visits that have eased the long diplomatic isolation of the territory’s Hamas rulers.
Hamas is also understood to be seeking guarantees Israel will stop its targeted killings, like the one that killed a top military commander on Wednesday, sparking the current hostilities.
Israel has its own demands, with Foreign Minister Avigdor Lieberman insisting “the first and absolute condition for a truce is stopping all fire from Gaza.”