A deadline of Sunday night passed after the two chief rebel groups refused to accept the deal, but AU mediators extended the discussions by a further 48 hours.
The US, which has accused the Khartoum regime and its allied Janjaweed militia of genocide against the local Darfur population, announced it was sending Deputy US Secretary of State Robert Zoellick to the talks in the Nigerian capital Abuja.
State Department spokesman Sean McCormack said the talks in Abuja had made progress in recent days toward 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," Mr McCormack said in a statement.
The rebels say the AU draft agreement also does not adequately resolve issues of power-sharing and wealth distribution in Sudan's vast western region, where some 300,000 people have died and 2.4 million others have been left homeless in the three-year-long conflict.
They also want a firm guarantee that the peace accord will be implemented.
Rebels reject deal
All four parties to the conflict, the rebel groups plus the Sudanese government and pro-Khartoum Janjaweed militias blamed for a raft of abuses in Darfur, were poised to sign the accord.
However two insurgent groups, the Sudanese Liberation Movement (SLM) and the Justice and Equality Movement (JEM), have rejected the deal.
"The extension of the deadline does not have any meaning for us," Saifaldin Haroun, spokesman of the main faction of the SLM, told AFP. "The AU peace proposal does not address our crucial demands."
Ahmed Hussain of his JEM group was "more interested in the concessions the government of Sudan will or can grant us during the extension. This will be the basis on whether or not we would sign the agreement."
Sudan said it would sign the deal in its current form and remain in Abuja until the Tuesday deadline had expired.
However, Sudan’s Vice President Ali Osman Taha was leaving the talks in Nigeria’s capital of Abuja, after apparently stating the Khartoum government's position.
Mr Taha would leave Abuja after he "has made clear the position of the national unity government with regards to the different issues", Mr Ahmed said.
Pressure from world leaders
The African Union has again urged the rebels to sign the peace deal it had brokered, saying further delay would only cause more suffering and "indiscriminate violence".
The AU hailed the Khartoum government's decision to accept the deal and said the rebel movements should do the same "in the interest of the Darfur people, who cannot take more suffering".
UN Secretary General Kofi Annan also called on the rebels to accept the deal, "so that the suffering and destruction in Darfur can be brought to an end."
Washington's envoy Robert Zoellick, who has already made four trips to Sudan, was to meet not only with parties to the Abuja talks but also the commanders of the AU peacekeeping force in Darfur.
The United States has been pressing to expand the underfunded 7,000-strong AU contingent in Darfur with a larger UN force able to count on NATO for beefed-up logistical and airlift support.
US Secretary of State Condoleezza Rice later urged world powers to step up action.