(CNN) -- The United States says that January's planned voting in Sudan on the southern region's independence should proceed as scheduled, despite a snag in talks over the status of a key oil-rich region.
U.S. Ambassador to the U.N. Susan Rice, among members of the Security Council who recently visited the country, said two planned referendums on self-determination must be held on January 9. She and other U.N. officials at the U.N. Security Council reaffirmed the call for a "timely holding" of the vote.
"The purpose of our visit was to underscore that the U.N. Security Council is united in its desire to see Sudan's referenda on self-determination carried out in accordance with the Comprehensive Peace Agreement," Rice said on Thursday.
The CPA was signed in 2005 to end the conflict between the northern-based government and the Sudan People's Liberation Movement/Army in the south.
"We delivered the message that the referendums should be held on time, that they should be credible, and that the results must be respected," she said.
The residents of southern Sudan will vote on whether to secede from country. And, residents of Sudan's Abyei area will vote on whether to be part of the north or the south.
But there has been an unsettled dispute over who should participate in the Abyei referendum, and because of these unresolved differences, officials from northern Sudan have expressed doubts that the voting will take place on time. There have also been concerns over lags in planning for the voting.
The North insists that the Missiriya, a nomadic Arab tribe, are eligible to vote in the Abyei referendum, but the South says only the permanently-based Dinka tribe should have a right to vote.
Media reports say the Missiriya tribe has warned of war if its members are barred from voting, and there are concerns over unrest among southerners if there's a delay in the vote.
Talks in Ethiopia failed to reach a breakthrough this week on Abyei.
U.S. State Department spokesman P.J. Crowley told reporters on Thursday that the United States continues "to believe that the parties should come together and fulfill their commitment to hold the Abyei referendum" on time. He didn't answer questions about whether the referendum should be postponed or the issue should be handled without a referendum.
There have been "important and constructive" talks on Abyei, "notwithstanding the absence of a final agreement," Crowley said. Nevertheless, he said, "there is work to be done," with the most important issue being voter eligibility.
He said that when the parties reconvene toward the end of October, Thabo Mbeki -- the former South African president who is the chairman of an African Union diplomatic team -- will facilitate the next round of discussions.
"So is it still possible? Yes. Is this going to be an enormous challenge? Yes. And we'll see what the parties are prepared to do when they reconvene on October 27," Crowley said.
More than 2 million people were killed in fighting between the North and South from 1983 to 2005, when a peace deal was finally brokered. That deal called for the referendum on independence in Southern Sudan.
CNN's Amir Ahmed contributed to this story.