At least 350 Palestinians have died in Gaza, local authorities say, after three days of heavy bombardment by Israel in what it says is a response to rocket attacks that have left at least three Israelis dead.
Ban, who said he respects Israel's right to self defence, said he was "deeply alarmed" by the violence from both Israel and the Palestinian Hamas group, which controls Gaza, adding, "This is unacceptable."
"All this must stop. Both Israel and Hamas must halt their acts of violence and take all necessary measures to avoid civilian casualties. A ceasefire must be declared immediately. They must also curb their inflammatory rhetoric."
On Monday, the White House reiterated its demands that Hamas stop firing rockets into Israel and agree to a ceasefire.
Gordon Johndroe, a spokesman for the White House, said in a statement on Monday that a ceasefire was "the objective to which all parties need to be working", including the US.
The US state department also said on Monday is was "vigorously engaged" in trying to restore the ceasefire between Hamas and Israel, after a six-month truce between the two sides expired earlier this month.
George Bush, the US president, is currently in Crawford, Texas where he is spending the New Year. His aides say he has been fully briefed on the latest events in Gaza.
He has not made any comment on the crisis since the bombing of the Palestinian coastal territory began on Saturday.
However, Bush did speak to King Abdullah of Jordan, telling him the US wants to see an end to the violence in Gaza , Johndroe said.
"Israel is going after terrorists who are firing rockets and mortars into Israel, and they are taking the steps that they feel are necessary to deal with the terrorist threat," he said.
Johndroe did not comment on whether the US believes that Israel is preparing a ground offensive in Gaza, saying that the Bush administration was taking the news "one day at a time".
However he added that the US "understands that Israel needs to take actions to defend itself".
Meanwhile Barack Obama, the US president-elect, who is also currently on holiday, is also said to be "monitoring" the situation, David Axelrod, his adviser, said on Sunday.