The leader of the Justice and Equality Movement (JEM), Khalil Ibrahim, rejected the AU as lead mediator and said his group would only accept the United Nations as principal mediator in any peace talks.
Ibrahim also called on UN troops to be stationed in Darfur.
The other main rebel group, the Sudan Liberation Army (SLA), said it was also dissatisfied with the AU but had not yet decided whether to attend a new round of talks in the Nigerian capital Abuja.
Ibrahim, speaking by telephone, said the AU had failed to hold the Sudanese government to account.
"JEM is rejecting the African Union. We are not going to Abuja again under the auspices of the African Union," he said.
The JEM and the SLA have been involved in faltering talks with the Sudanese government in Abuja to find a political solution to 22 months of conflict in the vast western region.
Intense fighting in South Darfur state over the past two weeks halted the Abuja negotiations, as each side blamed the other for starting the clashes. Thousands have fled the renewed violence.
The UN estimates more than 1
million people have been displaced
On 20 December, a previously unknown rebel group attacked an oilfield in the Darfur region of western Sudan.
"This was our first military operation and we chose the oilfields because this is the wealth of Sudan, which this government is not sharing with all of its people," said Ali Abd al-Rahim al-Shindy, leader of the Sudanese National Movement for the Eradication of Marginalisation.
Khartoum responded to the new fighting by mobilising troops for a major offensive, but halted its military efforts after intense pressure from the AU and the UN.
The Khartoum government said it would resume mobilisation if rebel forces did not disarm and withdraw from key locations. The JEM and SLA said Sudanese forces must halt all hostilities and withdraw first.
The Abuja talks have been near collapse since.
Hope for talks
Nevertheless, the AU has said the talks will resume some time in January. Spokesman Adem Thiam stressed on Thursday that the AU was still committed to finding a quick and lasting solution to the conflict despite the rebels' announcement.
"The AU will use the time to evaluate the whole process and assess AU's strategy and conduct consultations so as to restart the peace process on a much better basis," he said.