"In order for the violence to stop, Hamas must stop firing rockets into Israel and agree to respect a sustainable and durable cease-fire," White House spokesman Gordon Johndroe said during a news briefing at Bush's Crawford, Texas, ranch.
The administration also is concerned about the ability for humanitarian aid to reach Gazans, Johndroe said, adding, "We ask that all parties involved to allow food and medical supplies to reach the people there."
Israel launched an air assault on Gaza during the weekend, saying it was defending its citizens from rocket and mortar fire from Hamas militants. Since the airstrikes began, more than 300 people have died and more than 650 have been wounded. On Monday, militants fired at least 40 rockets and mortars from Gaza into Israel.
"We have urged the Israelis to avoid civilian casualties, but they are working on decreasing the number of Israeli citizens that are vulnerable," Johndroe said.
Bush has been in contact with leaders from the region as has Secretary of State Condoleezza Rice, he said.
Israel is targeting 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," Johndroe said. "Now, no one wants to see violence, but what we're going to need to see in order to end this is Hamas needs to stop firing rockets into Israel. And we all need to get to a sustainable cease-fire."