"A brighter future for Gaza and Israel depends on a sustainable ceasefire. It is up to the parties to live up to this responsibility," Ban's spokesman Stephane Dujarric in a statement.
"After 50 days of profound human suffering and devastating physical destruction, any violations of the ceasefire would be utterly irresponsible," Xinhua reported citing the spokesman.
The conflict in Gaza ended Tuesday after Israel and the Palestinians agreed on an open-ended ceasefire, putting an end to seven weeks of catastrophic loss of life.
"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.
"Any peace effort that does not tackle the root causes of the crisis will do little more than set the stage for the next cycle of violence," he stressed.
Israel launched a large-scale air, sea and ground military operations July 8 in Gaza in response to rockets fired into its land from the coastal enclave.
The Gaza health ministry said Israel has killed 2,140 Palestinians and wounded 11,100 others in the offensive.
On the other side, Israel said Gaza militants killed 69 Israelis, including 64 soldiers and five civilians.