The Sudan Liberation Army faction, led by Abdel Wahed Mohamed al-Nur, said it had rejected the whole peace accord - agreed by the main SLA leadership and Sudan in May - after the AU failed to meet its demands.
"The AU has absolutely and miserably failed in its efforts to mediate the fighting in Darfur," said Nouri Abdalla, an adviser to al-Nur.
"It is time it hands over the whole Darfur mediation file to the United Nations."
The demand is unlikely to be met as the UN has backed the AU sponsored agreement.
The Justice and Equality Movement , a smaller Darfur rebel group, has also rejected the accord.
In 2003, the Darfur rebel groups began their campaign in western region of Darfur, prompting an heavy-handed crackdown by the Khartoum government and its proxy militia - the Janjaweed.
The conflict has left about 300,000 people dead and 2.4 million homeless, with hundreds of thousands crossing the border into eastern Chad.
Al-Nur's faction has demanded that the AU attach supplementary documents addressing its concerns before it signs the deal.
But AU mediators and the government have refused to add or change the deal signed by Khartoum and the main SLA faction led by Minni Arcua Minnawi.
The faction led by Minnawi is stronger militarily, but the AU has urged al-Nur to sign because he represents the Fur, Darfur's biggest tribe.
They fear he may split the SLA along ethnic lines if he does not endorse the accord.