"We are talking constantly with the Israeli government to find a solution to Gaza that will be a sustainable one for the people of Gaza, for the people of Israel, and for the people of the Palestinian territories of the Middle East more broadly."
Rice also said she had no plans to visit the Middle East "at this point", but that she and the president were "in touch" with leaders of Arab states and Israel.
The US secretary of state's comments were echoed on Friday by Robert Serry, the UN's Middle East envoy, who said that Israel should open all crossings into the territory but that this would "require a commitment from Hamas that all rocket attacks and smuggling will end".
"A movement like Hamas if it ... wants to serve the interest of its people, it will have to listen to the calls for an end to the violence and they will have to play a very important role in that,' he said.
Ban Ki-moon, the UN secretary-general, is to host talks on Gaza with several Arab leaders next week at the organisation's headquarters in New York next week, including Mahmoud Abbas, the Palestinian president.
Also on Friday, a White House spokesman said that Israel has a right to defend itself against Hamas rocket attacks but that it must avoid civilian casualties.
Gordon Johndroe told journalists that the US also wanted Israel to ensure "that food and medical supplies reach the people of Gaza".
And in a US state department briefing also on Friday a spokesman said Hamas had violated the previous ceasefire with Israel and that the US hoped the Arab world "can understand our sincere efforts" to end the crisis.
Both Bush and Rice have been telephoning world leaders in recent days after Israel's aerial bombardment on Gaza began seven days ago in what it says is a response to rockets attacks from Gaza.
However, Bush has yet to make a public comment on the crisis, as has Barack Obama, the US president-elect, who takes office later this month.
Over the past seven days, 428 Palestinians and four Israelis have been killed.