The military wanted a 10-persons transitional council with seven of its members in uniform.
The coalition called for a "million march" to demand civil administration after differences with the ruling military council over the composition of the joint council.
They have been holding a sit-in outside the military headquarters in Khartoum and have also been negotiating with the council on the makeup of a transitional sovereign council for an interim period.
In an interview with AFP Wednesday, Sadiq al-Mahdi, Sudan s former premier and main political opponent of Bashir, warned protest leaders against provoking the military.
He said across the country six security personnel were killed during protests on Monday.
Sudan's public prosecutor has ordered the interrogation of ousted President Omar al-Bashir on suspicion of money laundering and financing terrorism, a judicial source told Reuters on Thursday.
In recent days, the DFC has held intensive discussions with the MTC with a view to persuading the latter to relinquish power to a civilian authority.
"We must not provoke the military council by trying to deprive it of its legitimacy or its significant role in the revolution", Al-Mahdi added. In turn, Vice President of the Military Council, Mohammad Hamdan Daklo, nicknamed Hamidati, said that the military council "is committed to negotiations, but will not allow chaos".
The spokesman for the military council, Lieutenant General Shamseddin al-Kabbashi, said the "armed forces must remain in the sovereign council" due to ongoing tensions in the country.
As the wrangling persisted, the crowds flocked to the army headquarters in central Khartoum to join the thousands who have remained camped there round-the-clock for weeks.
The Alliance is now demanding that the military council which took Bashir's place be replaced by a joint civilian-military council, although they say the number of members is yet to be finalised.
Others, referring to General Abdul Fattah al Burhan, the head of the ruling military council, chanted: "al Burhan you're dirty, you were brought by the Islamists".
Protest leaders from the Alliance for Freedom and Change want to replace that with a mixed body, but say the generals are not serious about handing power to civilians.
Since then, the Council has rejected calls to hand over power, prompting demonstrators to accuse the council's members of being no better than Al-Bashir.