The AU, which earlier extended the deadline for accepting the deal until midnight on Tuesday, said it called on all sides to put an end to the conflict.
"I must remind the leaders of the parties meeting in Abuja that each day that passes leads to more suffering and the deaths of innocent civilians from indiscriminate violence," said Alpha Oumar Konare, the AU Commission president.
Robert Zoellick, the US deputy secretary of state, has flown to join the peace talks in Abuja, Nigeria, in an attempt to rescue an agreement.
On Sunday, rebel groups announced they would not sign the deal in its current form.
The Sudanese government has accepted the AU's draft peace agreement and the country's chief negotiator said Sudan was ready to implement the deal whether the rebels accepted it or not.
"The African Union has to decide what steps should be taken if the current round [of talks] fails," chief negotiator Majzoub Khalifa said.
AU Commission Chief Alpha
"This would be a very regrettable situation. Anyone who obstructs peace efforts should be forced to bear responsibility."
Zoellick meanwhile will "try to assist the African Union mediation team find solutions to the remaining issues regarding a peace agreement for Darfur", Sean McCormack, a US State Department spokesman, said in a statement.
McCormack said the Abuja talks had made progress in recent days towards halting what the United Nations calls one of the world's worst humanitarian crises.
"Right now, it is down to a few difficult issues, things concerning disarmament of militias, how to integrate former militias into an armed force and associated issues," he said.
Rebel groups say the AU draft agreement also does not adequately resolve issues of power-sharing and wealth distribution in Sudan's western region.
They took up arms in early 2003 in ethnically mixed Darfur, an arid region the size of France, over what they saw as neglect by the Arab-dominated central government.
Khartoum used proxy militias drawn from Arab tribes to crush the rebellion.
The fighting has killed tens of thousands of people while a campaign of arson, looting and rape has driven more than two million from their homes into refugee camps in Darfur and neighbouring Chad.