Ban Wednesday said that he was alarmed by the new wave of violence that has engulfed Gaza, southern Israel and the West Bank, including East Jerusalem, Xinhua reported.
"The deteriorating situation in Gaza is leading to a downward spiral which could quickly get beyond anyone's control," Ban said.
The UN chief condemned the multiple rocket attacks launched from Gaza on Israel, stressing that such attacks are unacceptable and must stop.
He also urged Israeli Prime Minister Benjamin Netanyahu to exercise maximum restraint and to respect international obligations to protect civilians.
Israeli war jets launched a large-scale offensive on the Gaza Strip Tuesday with more than 100 air strikes on militant targets, killing 27 people and wounding 100 others.
The tensions along Israel's border with Gaza have escalated since the kidnapping and murder of the three Israeli teenagers, Eyal Yifrach, 19, Gil-Ad Sha'ar and Naftali Frankel, both 16.
Since Saturday Gaza militants have fired more than 300 rockets, projectiles and mortars from the Gaza Strip into Israel.
"Gaza cannot afford another full-blown war," Ban said.