The African Union (AU) has reaffirmed its intention to leave Sudan's Darfur region by the end of September when its truce monitors' mandate expires.
The Security Council had hoped UN troops would replace AU troops
The AU wants the UN to take over the mission, but Khartoum rejects this.
The UN has urged Sudan to accept its peacekeepers, as concern mounts over a new Khartoum offensive in the region.
Fighting between pro-government militia groups and rebels demanding greater autonomy has left hundreds of thousands dead and many more homeless since 2003.
"The AU Peace and Security Council met today (Monday) in Addis Ababa and decided to reaffirm that its mandate will end on 30 September in Darfur," Baba Gana Kingibe, the head of the AU mission in Sudan, said in a speech in Khartoum.
Sudan had said the AU peacekeeping force should leave Darfur unless it drops plans for the UN to take over its mission. It asked the AU to clarify its intentions.
UN spokesman Ahmed Fawzi said the international community was becoming increasingly impatient with the suffering in Darfur, where fighting between rebels and government forces has reportedly intensified.
Meanwhile, the International Rescue Committee says that one of its nurses was killed in fighting last Friday.
The 37-year-old Sudanese national was running a health centre in Hashaba, about 100km north of the North Darfur capital, el-Fasher.
The IRC says that 85,000 people in the area are now without health care.
The AU force has a weak mandate, is under-resourced, and numbers only 7,000 in an area the size of France.
AU deputy chairman Patrick Mazimhaka told the BBC that even if more money were forthcoming, political considerations made it difficult to stay longer.
Planeloads of Sudanese soldiers are now arriving in Darfur
He was speaking hours after Sudan said the AU troops could remain if they accepted Arab League and Sudanese government funding. Khartoum had earlier insisted the troops leave by the end of the month.
A UN resolution passed last week, seeking to replace the AU force with 17,000 UN troops, was rejected by Khartoum.
The government has said it will replace the peacekeepers with its own force of 10,000 soldiers to the region, but the UN and rights groups operating in the region have expressed alarm at this idea.
The AU brokered a peace accord in May, but it was signed by the government and only one of the three main rebel groups in Darfur.
Since then, the violence has intensified.
Sudan's President Omar al-Bashir described the call for a UN force as "part of a comprehensive conspiracy for confiscating the country's sovereignty" in comments reported by the Sudanese news agency Suna on Sunday.
Fresh Sudanese soldiers have been arriving in the region, and rights groups, AU officials and Darfur's rebel groups report that on 28 August a new offensive began, with reports of attacks on rebel-held villages in Darfur.
Khartoum has denied reports of bombing raids on villages, saying it is merely conducting "administrative operations".
Darfur refugees, rebels and the United States have long accused the Sudanese army of backing up the Arab Janjaweed militias in a "genocide" against the region's black African population.
Sudan has denied these claims and says the problems in Darfur have been exaggerated for political reasons.
Last week, the UN's humanitarian chief Jan Egeland warned that "a man-made catastrophe of an unprecedented scale" loomed within weeks in Darfur unless the UN Security Council acted immediately.
But analysts say sending a UN force to the region without Khartoum's consent would be a virtually impossible task - and few options now remain.