AU spokesman Nouredine Mezni said the leader of the Sudan Liberation Movement (SLM) faction has agreed to sign the accord, despite having some reservations on how power will be shared.
This comes hours after two other major Sudanese rebel groups fighting in Darfur refused to sign the peace deal with the government in Khartoum, despite intense international pressure to do so.
The chief negotiators of the Justice and Equality Movement (JEM) and the Sudanese Liberation Army (SLA) said the draft peace accord does not sufficiently address their demands.
JEM's Mohammed Tugod said the document does not answer his group's demands for Darfur's three states to be united into a single autonomous region.
"We clearly explained the reasons why this document failed to take into consideration the opinions of the movement and why the African Union mediation failed also to come out with a reasonable document," he said.
"We came to the conclusion that it's extremely difficult for us to accept this kind of document unless fundamental changes have been made... therefore we decided not to sign it," he told reporters in Abuja.
He said a peace deal sound include a larger provision to bring leaders from Darfur into the Sudanese federal presidency.
Abdelwahid Al-Nur of the SLA said the document needs to be improved before his group signs.
The refusals could jeopardise the peace process aimed at resolving the Darfur crisis which has cost an estimated 180,000 lives.
Talks dragged on for more than four hours past a midnight deadline after intense negotiations between international mediators, African Union officials, the Sudanese regime and rebel groups.
AU spokesman Nourredine Mezni said the talks will recommence on Friday morning, however the JEM leader said the issue of regional government is non-negotiable.
As drawn up by the AU, the proposed peace plan would call for a referendum in Darfur to decide whether to create an administrative region some time after fighting has halted and national elections have been held.
Khartoum has signalled that it would sign the AU document, which was rejected by the rebels on Sunday but which has since been modified following the intervention of US Deputy Secretary of State Robert Zoellick.
Mr Tugod welcomed Mr Zoellick's changes, but said they did not go far enough and would not be enough to convince the JEM to sign, and called on AU chairman President Denis Sassou-Nguesso to arrange further negotiations.
Decades of low-level tribal clashes over land and water in Darfur, a vast region about the size of France, erupted into large-scale violence in early 2003 with rebels demanding regional autonomy.
The central government is accused of responding by unleashing Janjaweed militias upon civilians, a charge Sudan denies.
At least 180,000 people have been killed and more than two million forced to flee their homes in what the UN has called the world's worst humanitarian crisis.
The conflict also has spilled into neighbouring Chad and the Central African Republic.
Revisions to the peace plan have called for 4,000 rebels to be integrated into Sudan's armed forces and another 1,000 into the police force, according to an AP report.
In addition, 3,000 rebels would be given training and education at military colleges.
The initial proposal mentioned no figures.
The new deal also would provide for rebels to comprise 33 percent of all newly integrated battalions nationwide, and 50 percent in areas to be agreed, notably Darfur.