The generals 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.
Both Ethiopian Prime Minister Abiy Ahmed and the African Union (AU) have been trying to mediate between the sides.
The council's spokesman, Lieutenant General Shams El Din Kabbashi, said on Sunday the council had rejected Ethiopia's proposal, which the opposition coalition agreed to on Saturday, but had agreed in principle to the AU's plan.
"The African Union's initiative came first," said Kabbashi, adding that the council had not studied the Ethiopian initiative, which he described as unilateral.
A draft of the Ethiopian proposal seen by Reuters 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.
Details of the AU proposal were not immediately known.
"We asked the mediators to unite their efforts and submit a joint paper as soon as possible to return the parties to negotiations," Kabbashi said at a news conference at the presidential palace.
Yasser al-Atta, a member of the military council, said: "The president (of the military council) clarified that he gave the mediators until tomorrow to present the joint vision."
Talks between the ruling generals and the Forces for Freedom and Change coalition collapsed when security forces stormed a protest sit-in outside the Defense Ministry on June 3, killing dozens.
The military said a crackdown on criminals spilled over to the sit-in area, but some officers have been detained for presumed responsibility.
The makeup of the sovereign council was the main outstanding sticking point between the two sides before the talks collapsed.
The military council canceled all agreements it had reached with the coalition after the sit-in's dispersal.
"The reality has changed, and calls for bringing other political forces, together with the Forces for Freedom and Change, into government," Atta said on Sunday.