Khartoum's Vice President Ali Osman Taha and the head of the Sudan People's Liberation Army (SPLA) resumed discussions on Friday after failing to meet a self-imposed end-of-year deadline for sealing a peace deal.
"The two parties resumed talks at 11:00 am (0800 GMT) after a one day break," Lazaro Sumbeiywo, a retired Kenyan army general mediating the talks, said.
Before adjourning for the New Year and Sudan's Independence Day, mediators reported both parties had made progress on the status of the three disputed areas of Abyei, southern Blue Nile State and the Nuba Mountains.
The southern-based SPLA claims these areas although they are not geographically part of the south.
The two sides had "broadly agreed" that the southern Blue Nile State and the Nuba Mountains regions would remain autonomous.
But they had not reached a deal "on the extent and nature of the autonomy" as well as the status of Abyei, a member of the mediating team said Friday.
Also under discussion is power-sharing - mainly the distribution of political and administrative posts.
And the two sides are discussing the status of the capital, Khartoum, particularly whether Islamic law would apply in the city during an envisaged transition period.
Sudan is the scene of Africa's
longest civil war
Khartoum and the rebels have already reached a rough agreement on the sharing of wealth, particularly oil revenues. Most of Sudan's oil is in the rebel-held south.
In 2002, Khartoum and the SPLA struck a breakthrough accord granting the south the right to self-determination after a six-year transition period.
And last September both sides reached a deal on transitional security, under which the government would withdraw its troops from southern positions.
The war in Sudan, which erupted in 1983, is the longest-running civil conflict on the African continent.
It has pitted the south, where most observe traditional African religions and Christianity, against the Muslim, Arabised north.
The conflict has claimed at least 1.5 million lives and displaced an estimated four million people.