The ruling generals and the coalition have been wrangling for weeks over what form Sudan's transitional government would take after the military deposed long-time president Omar al-Bashir on April 11.
Both Ethiopian Prime Minister Abiy Ahmed and the African Union have been trying to mediate between the sides.
The council's spokesman, Lieutenant General Shams El Din Kabbashi, said on Sunday the council has rejected Ethiopia's proposal, which the opposition coalition agreed to on Saturday, but had agreed in principle to the AU's plan.
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.
Talks between the ruling generals and the coalition collapsed when security forces stormed a protest sit-in outside the Defence 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.