The Bush administration's comments come as Ban Ki-Moon, the United Nations secretary-general, urged all sides to "halt acts of violence" and take measures to end civilian casualties.
The UN secretary-general condemned the violence as "unacceptable" and put pressure on both Arab and world leaders to act "swiftly and decisively" to end the impasse between the two sides, saying leaders "must also step up efforts to support a longer term resolution of the issue".
Ban also said that both sides should calm their rhetoric in a bid to restart dialogue on a possible ceasefire and said Israel should keep all of Gaza's crossings open so that aid could flow into the territory.
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 but in a durable way, 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.