Ban, however, said that any peace effort which does not tackle the root causes of the crisis will do "little more than set the stage for the next cycle of violence".
"Gaza must be brought back under one legitimate Palestinian Government adhering to the PLO commitments; the blockade of Gaza must end; Israel's legitimate security concerns must be addressed," a statement issued by Ban's spokesperson said.
"After 50 days of profound human suffering and devastating physical destruction, any violations of the ceasefire would be utterly irresponsible," the statement said.
"The Secretary-General remains hopeful that the extended ceasefire will act as a prelude to a political process as the only way of achieving durable peace," the statement said, adding that the two-State solution is the only viable option.
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"The Secretary-General urgently calls on both parties to return to meaningful negotiations towards a final status agreement that addresses all core issues and ends the 47-year occupation."
Ban said after the latest round of killing and further widespread destruction of Palestinian homes, civilians on both sides need a reprieve in order to resume their daily lives, and to allow for humanitarian and early recovery efforts to address the desperate needs of the people in Gaza.
The ceasefire deal mediated by Egypt calls for opening up Gaza border crossings, lifting fishing restrictions, the reopening of the Gaza airport and lifting the blockade.