Ban reiterated his call for an end to the fighting, which he said had "grave implications for the safety of both Israeli and Palestinian civilians," his press office said in a statement.
The U.N. Security Council called on Saturday for a ceasefire.
"The Secretary-General does not believe that what is inherently a longstanding, serious political dispute between Israelis and Palestinians can be resolved via military means by either side," the statement said.
Thousands fled their homes in a Gaza Strip town on Sunday after Israel warned them to leave before it attacked rocket-launching sites, on the sixth day of an offensive that Palestinian officials said had killed at least 160 people.
Militants in Hamas-ruled Gaza kept up rocket salvoes deep into the Jewish state as the worst bout of Israel-Palestinian bloodshed in two years showed no signs of abating, and Western foreign ministers said a ceasefire was an urgent priority.
Ban said indiscriminate firing of rockets on Israeli civilian targets by Hamas was a violation of international law and that he was "deeply worried about the impact on Palestinian families of Israeli military action."
"Too many Palestinian civilians have been killed, and any Israeli ground offensive will undoubtedly increase the death toll and exacerbate civilian suffering in the Gaza Strip," the statement said.
"The Secretary-General feels a sense of responsibility for the Palestinians who, especially in the Gaza Strip, have long been denied the sense of freedom and dignity that they deserve," it said, adding that Ban "remains engaged with both sides to urge de-escalation and an end to violence."
"He strongly believes that it is in the interest of both sides that steps toward dangerous escalation be replaced with immediate measures to end the fighting, thus preventing further casualties and greater risks to regional peace and security," the statement said. "He demands both sides move in this direction now."