The under equipped AU force of 7,000 had been due to handover to the UN at the end of September.
Sudan, however, has so far refused to allow UN peackeepers into the country.
Kofi Annan, the UN secretary-general, asked the AU to extend its mission during their weekend conference in the Gambia capital Banjul.
"On the request of the secretary-general, the African Union will continue to fulfil its mission until the end of the year," said Sassou Nguesso, the president of the Congo Republic, who holds the rotating AU presidency.
Annan met the Sudanese president, Omar Hassan al-Bashir, on the fringes of the summit but failed to persuade him to allow UN troops into Darfur
Annan described the crisis there as "one of the worst nightmares in recent history".
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.