Rice is in the Middle East partly to support Mahmoud Abbas, the Palestinian president, in his struggle with Hamas over plans to form a unity government.
Ismail Haniya responded to Abbas's suggestion that he might dissolve the Hama-led government over its failure to reach an agreement by telling him on Wednesday "to avoid using the sword of time" by setting any deadlines in unity discussions.
"There is an elected Palestinian government which expresses the will of the Palestinian voter. However, we have said we do not have a problem to resume the dialogue to form a unity government," Haniya said.
Abbas has made clear that his patience is running thin in efforts to persuade Hamas to soften its policy towards Israel and join with his Fatah faction.
"If this doesn't happen in the near future, all options are open," he said at a news conference with Rice. "But the only option I reject is civil war".
Rice told the news conference in Ramallah that the Palestinians should be served by a government "that observes the Quartet principles and that can form the basis then for movement forward on what we all desire ... And that is a two-state solution, a solution in which a democratic Palestine and a democratic Israel can live side by side in peace".
Abbas's chief of staff said the president had given Rice a "working paper" to take to Israel suggesting ways to move towards a resumption of peace talks and ease Israeli restrictions on Palestinian trade and travel.
"There is an elected Palestinian government which expresses the will of the Palestinian voter. However, we have said we do not have a problem to resume the dialogue to form a unity government".
Palestinian prime minister
Rice said she and Abbas had discussed ways to "make possible a life for the Palestinian people that is not subject to the kind of daily humiliations that we know have been associated with the occupation".
One senior Palestinian official who attended the meeting between Rice and Abbas told Reuters news agency that "there was a lot of talk on the next Palestinian government".
The official said that Abbas wanted Hamas to agree to a political platform that recognises Israel, renounce violence and abide existing peace deals. "President Abbas told her [Rice] he has given Hamas less than two weeks to give him an answer," he said.
Rice will travel to Israel on the next leg of her regional tour for talks with Ehud Olmert, the Israel prime minister, and her Israeli counterpart, Tzipi Livni.