Ban said it is in the interest of both sides that "steps towards dangerous escalation be replaced with immediate measures", thus preventing further casualties and greater risks to regional peace and security, Xinhua reported.
Ban said he was alarmed that despite the UN Security Council's clear demand for a ceasefire, the situation in and around Gaza has worsened with grave implications for the safety of both Israeli and Palestinian civilians.
Moon expressed deep worry about the impact on Palestinian families
The UN chief expressed deep worry about the impact on Palestinian families of Israeli military action, saying too many Palestinian civilians have been killed, and any Israeli ground offensive would undoubtedly increase the death toll and exacerbate civilian suffering.
Since Israel began Operation Protective Edge last Tuesday in order to stop rocket attacks from Gaza, 170 Palestinians have been killed and 1,154 were injured.
The UN estimates that about 80 percent of the casualties were civilians.
Concerned about the ongoing crisis, the UN Security Council on Saturday issued a press statement calling for a ceasefire between the Israelis and Palestinians and the protection of civilians.