The Transitional Military Council (TMC) and the opposition coalition have been wrangling for weeks over what form Sudan's transitional government should take after the military deposed long-time President Omar al-Bashir on April 11.
On Sunday, Shams al-Din Kabashi, spokesman for TMC, said the council rejected the Ethiopian initiative but had agreed in principle to the AU's plan.
Details of the AU proposal were not immediately known.
A draft of the Ethiopian proposal, seen by the Associated Press and Reuters news agencies, suggested that a ruling sovereign council would be made up of seven civilians and seven members of the military, with one additional seat reserved for an impartial individual.
Ahmed Rabie, spokesman for the opposition Alliance for Freedom and Change, said the council was to have a rotating chairmanship. The majority of the civilians on the interim body would come from the alliance, he told AP.
"We asked the mediators to unite their efforts and submit a joint paper as soon as possible to return the parties to negotiations," Kabashi said at a news conference at the presidential palace.
This joint proposal should be received by Monday, he said.
Ethiopia and the AU have stepped up diplomatic efforts to resolve the crisis in Sudan.
Talks between the TMC and the Alliance for Freedom and Change collapsed when security forces stormed a protest sit-in outside the defence ministry on June 3, killing scores of protesters.
A member of the military council, Yasser al-Atta, suggested that it had doubts about the protest leaders ability to govern.
He addressed protest leaders saying that "you should include other political forces" or it would be difficult to rule.
"We want them to rule and lead the transitional period, but can this be done?" he added.
Egypt has voiced its support for the military council, pressing the African Union not to suspend Sudan's activities in the regional block. Saudi Arabia and the UAE have pledged $3bn in aid to shore up its economy.
Sudanese activists fear that the three countries are pushing the military to cling to power rather than help with democratic change, given that the three Arab states are ruled by leaders who have clamped down on political freedoms in their own countries.
On Saturday, leaders of the umbrella protest movement said they accepted the creation of a civilian-majority governing body for a political transition in Sudan.
The alliance said their approval of the Ethiopian plan "pushes all the parties to bear their responsibilities" to find a peaceful solution, and urged the military council to accept the plan "in order to move the situation in Sudan" forward.