The rebel faction kidnapped a multi-national AU ceasefire monitoring team on Sunday and their rescue team.
AU spokesman Noureddine Mezni on Monday said the military head of the AU mission had personally witnessed the release of 36 of the hostages.
"According to our information and with some reservation, we can say that there was a happy ending as most hostages were released," Mezni told AFP.
Two remaining hostages were released a few hours later.
Mezni said the AU mission's Commander-in-Chief Festus Owkonko was heading to Tine, where the abductions took place Sunday near the border with Chad, to assess the situation on the ground.
The kidnappers were thought to be members of a dissident faction of Darfur's rebel Justice and Equality Movement (JEM), Mezni said.
Saturday's clashes caused the
first AU casualties in Darfur
But the head of the JEM's negotiating team at peace talks in the Nigerian capital, Abuja, said that the insurgent leader they think to be behind the kidnapping had been drummed out of the movement.
"Mohammed Saleh is not a member of JEM. We kicked him out almost six months ago, and right now he's across the border in a neighbouring country," Mohammed Tugod said, apparently referring to Chad but declining to do so explicitly.
"I think this act has been done by Mohammed Saleh, and now we are trying to investigate and find out where he has gone with these people," he said.
Chad, which had 10 soldiers among those kidnapped, condemned the kidnapping as an "indefensible and barbaric act", and its foreign minister called for the immediate release of the hostages.