The latest row has heightened distrust at the talks, a day after they were officially launched at a luxury hotel in Nigeria's capital, Abuja.
African Union (AU) negotiators are in intense consultations with the parties to resolve the issue, AU spokesman Mezni Nourredine said.
The dispute between Sudan's government and the two rebel groups over the presence of Eritrea and Chad prevented a scheduled meeting on Saturday, where the African Union's special envoy for Darfur was due to chair a discussion on the talks' agenda.
Delegates said Sudan was objecting to the presence of Eritrea - seen as close to the rebels - as an observer.
"There are procedures for admission, and all parties have to be consulted," said Sudan's ambassador to Nigeria, Abd al-Rahim Ahmad Khalil, when asked whether he objected to Eritrea's presence. He declined to comment further.
Meanwhile, the delegation from Sudan's western neighbour, Chad - a key mediator in the talks - has not arrived.
Millions have fled the fighting
A Western diplomat said Chad's absence was linked to a dispute with the rebel Justice and Equality Movement (JEM), which says Chad should withdraw from the talks as it is too close to Sudan's government.
However, Chad's top negotiator, Allam Mi-Ahmed, said he had been delayed only because no planes were available, and he would arrive by Monday.
At the same time, Mi-Ahmed attacked the JEM delegation - which is dominated by Darfur exiles - as being "hotel opponents" who had little on-the-ground experience.
He also complained that the African Union had not invited an alternative Darfur-based leader, Mohammed Saleh Hakim.
Previous peace accords have so far failed to end conflict in Sudan's western Darfur region, which has led to an estimated 180,000 deaths.
Sudanese officials have said the government is determined to resolve the crisis this time.
But they are also opposing the UN-backed International Criminal Court's recent investigation of war crimes in Darfur. The government said it would conduct its own trials.
Sudan institutes court
On Saturday, Sudanese Chief Justice Jalal el-Din Mohammed Othman ordered the establishment of a special criminal court to consider war crimes in Darfur, Aljazeera reported.
"The JEM should have moved its men out earlier. We had to intervene to get them released"
The court, which will begin its work later this week, has been empowered to rule on all human rights violations and war crimes, a statement issued by the chief justice said.
AU garrison raided
Meanwhile, Sudanese armed forces on Saturday raided a garrison of AU peace monitors at al-Fashir in Darfur and arrested three members of the JEM, who were in the camp, said Nigerian General Festus Okonkwo, commander of the peacekeeping and observer mission.
"The JEM should have moved its men out earlier. We had to intervene to get them released," he said, adding: "They were released a few hours later."