"I think it can help all of us to have a destination in mind," Rice said. "I think this time it is best to talk about that political horizon in parallel. But I sincerely hope in the future the parties themselves can talk about the political horizon themselves."
 
Rice is travelling to the Middle East to pursuade Arab states and Israeli to renew peace efforts following the formation of a Palestinian unity government earlier this month.
 
Abbas hails new US effort
 
Abbas told journalists that he was satisfied with the renewed US mediation efforts, which have not produced tangible results. Abbas said he talked with Rice about holding more meetings with Olmert.
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"All these meetings are part of the bilateral relations with Israel and the future vision that we are all seeking and working toward," Abbas said.
 
Earlier Sunday, Abbas met with Ban Ki-moon, the UN chief, who said the time is "not yet fully ripe" to meet with officials from the Islamic militant Hamas group.
 
Ban met with non-Hamas members of the new coalition, while Rice snubbed even U.S.-backed moderates in the Cabinet.
 
Hamas and Fatah have expressed hope their alliance would end international isolation of the previous hard-line Hamas government.
 
Rice said she would meet twice with both Abbas and Israeli Prime Minister Ehud Olmert during her fourth trip to the region in as many months.