The latest announcement appears to reverse Khartoum's ultimatum on Sunday to AU peacekeepers to leave after September 30.
One African diplomat said the government softened its position because it realised expelling the AU would end implementation of an AU-brokered May peace deal between Khartoum and a rebel faction fighting government-supported militias.
But on Monday night, the AU said it will end the mandate of its troops in Darfur on September 30.
"The AU Peace and Security Council met today in Addis Ababa and decided to reaffirm that its mandate will end on September 30 in Darfur," Baba Gana Kingibe, the head of the AU mission in Sudan, said.
A US-British-backed UN resolution, which Khartoum rejects, says more than 20,000 UN troops should take over peacekeeping from AU forces.
Sudan is against the AU mission being turned over to the UN.
AU troops were expected to fill the gap before the arrival of the UN and ultimately be absorbed into the UN operation, according to the resolution passed last Thursday.
But Mustafa Osman Ismail, a presidential adviser, said on Monday that the UN mandate's goal was "regime change" in Khartoum.
"Sudan will not accept those troops to be transformed into part of a UN force," Ismail said.
Referring to resolution clauses, he said: "Monitoring the borders ... protection of civilians ... creating an independent judiciary has all become the responsibility of the international forces, so what is left for the government?"
"The United States has a clear strategy ... of trying to weaken this government ... or trying to change the government."
A Sudanese foreign ministry spokesman on Sunday had said that AU troops monitoring a shaky truce in Darfur must leave when their mandate expired on September 30.
The fighting in Darfur began when mostly non-Arab rebels took up arms against the government, accusing it of marginalisation and neglect. Since then, tens of thousands of people have been killed.
Washington calls the rape, pillage and murder that has forced 2.5 million people from their homes "genocide", and blames the Sudanese government and its allied militia known locally as Janjaweed.
Khartoum rejects the charge but the International Criminal Court (ICC) is investigating alleged war crimes in Darfur.
Critics say Khartoum fears UN troops would be used to arrest officials likely to be indicted by the ICC.
The European Union's executive Commission called on Sudan on Monday to recognise the broad international agreement that the AU should hand over to a stronger UN mission because of the deteriorating humanitarian situation in Darfur.
Former rebels, now part of government with the dominant National Congress Party, said they did not agree with the decision to ask the AU to leave and had not been consulted.
Minni Arcua Minnawi, leader of the former Darfur rebel Sudan Liberation Movement (SLM), which joined the government after the May peace deal, was quoted by local papers as calling the decision "a violation of the Darfur peace deal".