Abbas has called for a ceasefire between Israel and the Hamas movement, which took full control of Gaza when it routed his security forces since last June.
But at a news conference with her Israeli counterpart Tzipi Livni, Rice said that a truce was not a condition for the resumption of talks.
"I have been informed by the parties that they intend to the resume the negotiations and that they are in contact with one another as to how to bring this about," she said.'Mutual calm'
A statement issued by Abbas's office after the news conference said that Rice was exerting efforts to "enforce a mutual calm" and Abbas's intention was to "resume the peace process and the negotiations".
According to the Palestinian news agency Wafa, Abbas and Rice agreed last night that a truce - to be mediated by Egyptian officials - should be reached as soon as possible.
The understanding also reportedly included a commitment by Abbas that he would take part in a trilateral US-Israeli-Palestinian meeting to implement the first phase of the road map.
Hamas officials told Al Jazeera that they are open to Abbas's initiative "but he has to talk to us first".
Rice urged Hamas to halt the frequent rocket attacks from the Palestinian territory.
"There is a need to restore calm, and that of course that means also stop the rocket attacks against Israeli citizens. We have talked about the need to return to the path of negotiations."
"There are enemies of peace that will always try to hold hostage the Palestinian cause and the future of the Palestinian people," she said. Rocket attacks
Ehud Olmert, the Israeli prime minister, has said that Israel will end the military offensive if the cross-border rocket attacks are halted.
"One thing should be clear: If there is no Qassam [rocket] fire on Israel, there will be no Israeli attack on Gaza. We do not rise in the morning and think about how to attack Gaza," he said.
Rice met Palestinian negotiators in the occupied West Bank on Wednesday before meeting Livni and Ehud Barak, Israel's defence minister.
Meanwhile, the Arab League, meeting in Cairo
, threatened to withdraw the Arab peace initiative over the Israeli attacks, condemning them as "brutal crimes".