The postponement was aimed at giving more time for discussion of proposals from the delegation of the Justice and Equality Movement (JEM), one of the two main rebel groups, on the Declaration of Principle (DoP), a mediation team spokesman, Sam Ibok, said.
"Yes, we are desperate over the issue," Ibok said. "We owe it to the people of Darfur to make sure that these talks are concluded."
He said that the plenary session earlier scheduled to resume Tuesday had been delayed by 24 hours to give more time to the discussions on the JEM paper. The JEM's hostility to Chad and its views on the DoP have been preventing movement in the talks.
"The DoP is preliminary to the negotiations. The issue of Chad is being handled by AU chairman and Nigeria's President Olusegun Obasanjo in consultation with other African leaders," Ibok said.
The DoP lays the groundwork for a political deal and reaffirms the principles of unity, sovereignty, the territorial integrity of the country, federalism, respect of diversity and the end of impunity for those committing serious human rights offences.
Later discussions will centre on power sharing, the distribution of wealth and security agreements. But the presence of Chad remains an obstacle to progress.
"Our position is the same. It has not changed. Chad is not impartial and not neutral. They are responsible, along with the government of Sudan, in committing genocide in our country," JEM's spokesman, Ahmed Hussain Adams, told a group of reporters after his group's meeting with partners and AU mediators.
After lengthy negotiations, the other main Darfur rebel groups, the Sudan Liberation Movement (SLM), dropped its opposition to Chad's participation.
"It is the considered view of the SLM negotiating delegation that it has come to Abuja not to wade into the controversy or argument of whether Chad should be mediator or not, but to help negotiate and achieve peace," the group said late Monday.
"The issue of Chad in the resolution of the crisis is beyond what we can handle. It is being handled by Obasanjo who is busy consulting with his peers: Idriss Deby of Chad, Muhamar Ghaddafi of Libya and AU Commission chairman Alpha Oumar Konare", Ibok said.
"We are hoping that they will be able to find an arrangement which will allow us to conduct the talks under the auspices of the chairman of AU with the direct mediation of AU special envoy on the Darfur talks, Tanzanian Salim Ahmed Salim", he added.
He said he felt both "desperate and optimistic" about the chances of reaching a deal.
Earlier Tuesday, the AU held a meeting with its international partners and observers, including Chad and Eritrea, whose presence is opposed by the Sudanese government.
Fighting has raged in Darfur since February 2003, when local armed groups launched a rebellion in the name of the region's black African tribes, alleging discrimination and persecution by Khartoum's Arab-dominated government.
Since the war began, between 180,000 and 300,000 people are thought to have been killed and 2.4 million displaced from their homes. Some 200,000 have fled into Chad.