Rice, attending a regional meeting on Iraq's security and future, contradicted Carter's assertions that he never got a clear signal from the State Department. Rice told reporters that the U.S. thought the visit could confuse the message that the U.S. will not deal with Hamas.
"I just don't want there to be any confusion," Rice said. "The United States is not going to deal with Hamas and we had certainly told President Carter that we did not think meeting with Hamas was going to help" further a political settlement between Israel and the Palestinians.
Carter said top Hamas leaders told him during seven hours of talks in Damascus over the weekend that they are willing to live next to Israel, but a top Hamas official said the group would never outright recognize the Jewish state.
Separately Tuesday, a Hamas official said the militant group has softened its demands for a cease-fire with Israel.
Spokesman Ghazi Hamad said Hamas is nowthat would only include the Gaza Strip.
The group previously has demanded the West Bank be included in any deal. Still, it hopes a Gaza truce will eventually spread to the West Bank as well.
In return, Hamas wants Israel and Egypt to open their trade and passenger crossings with Gaza. The border has been sealed since Hamas violently seized control of Gaza last June.
Israel also considers Hamas a terrorist group.
On Tuesday, Israel reopened a Gaza border crossing, sending 90 trucks loaded with supplies to the Palestinians. The resumption of deliveries came three days after Hamas militants launched a failed car bomb attack on a separate cargo crossing, reports CBS News correspondent Robert Berger from Jerusalem.
Israeli officials say Hamas is trying to force Israel to cut off supplies, thereby sparking a humanitarian crisis in Gaza to win international sympathy and bring condemnation on the Jewish state, Berger reports.
Carter won no specific concessions from Hamas. He defended his trip during remarks Monday in Jerusalem. He said he failed to convince the top Hamas boss, Khaled Mashaal, that he could gain international goodwill if he stopped rocket fire on Israel for one month.
"I did the best I could," Carter said. "They turned me down, and I think they're wrong."
In an interview with NPR, Carter said the State Department did not warn him off the trip. A State Department spokesman in Washington took issue with that on Monday, and Rice was more blunt in her account Tuesday.
Rice had heard questions about Carter's meetings several times during two days of Iraq-themed meetings in the Mideast, with some diplomats wondering whether the Bush administration was talking to Hamas through the back door or contemplating a different policy in the future.
Rice said U.S. policy remains that it will deal only with the elected Palestinian president, Mahmoud Abbas, and his West Bank-based government as it tried to help Israel and the Palestinians broker terms for an independent Palestinian state.