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(CNN) -- The leaders of Sudan and South Sudan met Sunday in Ethiopia, attempting to resolve -- under international pressure -- issues arising from the latter nation's independence just over a year ago.
The creation of South Sudan stemmed from a referendum, agreed to by leaders in the Sudanese capital of Khartoum, in which people in the southern part of the landlocked African nation voted for independence.
South Sudan formally became a new nation in July 2011, though significant issues with Sudan remain. Chief among them are the demarcation of the border between them, the possible creation of a demilitarized zone and the transportation and processing of oil from South Sudan, which got around 70% of the formerly united country's reserves when it became independent.
On Sunday, top officials from the two countries, including South Sudan President Salva Kiir Mayardit and Sudan President Omar al-Bashir, met at the Sheraton Hotel in Addis Ababa in an attempt to bridge these differences.
Speaking from Ethiopia, Sudanese official Badreldin Abdalla said there had been "progress" in the talks, which were broken into different "clusters" reflecting the specific issues being discussed.
"They are going to have very substantive meetings to finalize the negotiations," Abdalla said.
At the United Nations headquarters in New York, Sudan's ambassador to the U.N., Dafalla Al-Haj Yousif, likewise pointed to what he described as "good progress in all the issues discussed between the two parties."
Members of the delegations plan to talk with officials in their respective capitals, then to meet again soon to ideally move even closer to a final resolution, he said.
His South Sudanese counterpart at the United Nations, Francis Nazario, said his nation is committed to reaching an agreement in accordance with a U.N. resolution "and the African Union roadmap" -- which lays out details for a possible final deal, including setting up a demilitarized zone along the two countries' border.
But Nazario said Sudan was not on board, at least yet.
"The Republic of South Sudan is concerned that the Sudan negotiating team has not accepted the African Union road map for the purpose of setting up the demilitarized zone," he said.
U.S. Ambassador to the United Nations Susan Rice called Sudan's refusal to "accept ... the map" was "an issue of utmost concern." She said the international community is prepared to act to spur the countries to reach a resolution.
"Our aim is not to propose sanctions," Rice said. "Our purpose is to spur the parties to meet their obligations and to create a foundation for lasting peace."
Peter Wittig, Germany's U.N. ambassador and the current president of the U.N. Security Council, noted the governments have failed to reach a peace deal in the past but said they cannot afford to let the disagreements linger.
"Council members shared the view that the suffering of the people ... requires that both sides act with a sense of urgency, and both parties should not allow technicalities to stand in the way," said Wittig.
"There's a great awareness that there's not much time left."