Atabani quit after he was replaced at the talks by Sudanese First Vice President Ali Osman Taha, Egypt’s al-Ahram newspaper said.
Taha took over talks with Sudan People's Liberation Army (SPLA) leader John Garang in a bid to break the deadlock between the two sides.
International pressure to end Africa’s longest civil war has mounted in recent weeks.
Sudan, Africa's largest country, has been battered by civil unrest since independence in 1956. The current war started in 1983 when the SPLA took up arms.
More than 1.5 million people have died as a result of fighting. The war has also displaced more than four million others.
“The whole world is putting pressure on Khartum and the SPLA to reach a peace agreement," said Kenyan Foreign Minister Kalonzo Musyoka.
Talks between the two sides continued through Friday.
"I am very optimistic that the consultations between the two leaders will make progress"
Kenyan foreign minister
"They are determined to bring peace to their country and have agreed that this process is irreversible," said Musyoka.
"Delegates surely cannot go to the next round of talks with good morale if these two leaders fail to agree," said Eritrea's ambassador to Kenya Mohamed Omaro, who is mediating at the negotiations.
History of breakdowns
Discussions have been marred by numerous breakdowns.
Khartum on 23 August rejected a draft final document unveiled by Intergovernmental Authority on Development (IGAD) saying the plan would result in the South proclaiming independence.
Were talks to breakdown again, one mediator who declined to be identified said IGAD would propose that both leaders form a committee to draft a new framwork.
The main sticking points are security arrangements, wealth-and power-sharing and the disputed areas of Southern Kordofan, Abyei and the Southern Blue Nile.
"I'm very optimistic that the consultations between the two leaders will make progress. I'm very encouraged by the statement by Garang when he arrived in Kenya that they have come to unlock the peace process," Musyoka said.
Fighting in west Sudan
Separately, rebels in Darfur, west Sudan, said the government on Friday attacked their bases some 24 hours before a six-week ceasefire was due to come into effect.
The Sudanese government and the SLM rebels signed a six-week ceasefire on Wednesday in Chad.
Some hundreds of people have died in clashes between the two sides in the semi-arid region bordering Chad in recent months.
The SLM is not party to negotiations in Kenya.