Ban said he had spent the day talking with world leaders including Israeli Prime Minister Benjamin Netanyahu, Palestinian president Mahmud Abbas and Egypt's President Abdel Fattah al-Sisi, as well as US Secretary of State John Kerry.
It came as Israeli warplanes pounded Gaza, killing dozens in a major new confrontation with Palestinian militants, as Hamas flexed its firepower and sent thousands running for shelters across the country.
"I am alarmed by the new wave of violence that has engulfed Gaza, southern Israel and the West Bank -- including East Jerusalem. This is one of the most critical tests the region has faced in recent years," said Ban.
"Gaza is on a knife edge. The deteriorating situation is leading to a downward spiral which could quickly get beyond anyone's control.
"The risk of violence expanding further still is real. Gaza, and the region as a whole, cannot afford another full-blown war. "
Ban condemned the rocket attacks launched from Gaza on Israel, saying: "Such attacks are unacceptable and must stop."
He said he had also urged Netanyahu to exercise maximum restraint and to respect international obligations to protect civilians.
Israel PM warns of tougher action
Israeli Prime Minister Benjamin Netanyahu appears bent on ploughing ahead with its attacks on Hamas, warning of even tougher action.
Israeli warplanes have pounded Gaza, killing at least 30 people in a major new confrontation with Palestinian militants, as Hamas flexed its firepower and sent thousands running for shelters across the country.
As the death toll from Israel's two-day Operation Protective Edge reached 57, Palestinian president Mahmoud Abbas accused Israel of committing "genocide" in Gaza.
But Israeli Prime Minister Benjamin Netanyahu appeared bent on ploughing ahead, warning of even tougher action against Hamas.
There have been no Israeli deaths so far, but Hamas began flaunting its firepower overnight, launching waves of long-range rockets across central Israel that triggered sirens in cities as far away as Tel Aviv and Jerusalem.
The alarms even sounded in the northern port city of Haifa, as unconfirmed reports spoke of a rocket hitting near Caesarea, and another even further north.
Tanks massed on the Gaza border, AFP correspondents reported, as Netanyahu came under mounting pressure from hardliners within his governing coalition to send ground forces into the territory from which it pulled all troops and settlers in 2005.
"We have decided to further intensify the attacks on Hamas and the terror organisations in Gaza," his office quoted him as saying.
President Shimon Peres, who retires later this month, was quoted by his office as saying in an interview with CNN that, "if the fire continues we do not rule out a ground incursion," adding this "may happen quite soon".
The escalation comes with Arab riots inside Israel over the burning to death of a Palestinian teenager by Jewish extremists and the region in flames, with civil war raging in neighbouring Syria and conflict intensifying in Iraq.
The Palestinian teenager was murdered in apparent revenge for the kidnap on June 12 of three Israeli youths in the occupied West Bank, who were subsequently killed.
Six women and nine children were among at least 30 Palestinians killed in Israeli strikes on Gaza on Wednesday, medics said.
So far, neither side has shown any sign of backing down, as Israel stepped up its preparations for a possible ground assault, approving the call up of 40,000 reservists.
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