The Forces for Freedom and Change (FFC) coalition has called for a million people to take to the streets of the capital, Khartoum, to press its demands for the military council to cede power to civilians.
The generals and the opposition movement have been wrangling for weeks over how to manage a transition towards elections following the military's ouster of long-time President Omar al-Bashir on April 11.
"We warn of the seriousness of the crisis our country is going through," the council said in a statement carried by state news agency SUNA.
"We also hold the Forces for Freedom and Change fully responsible for any spirit that is lost in this march, or any damage or harm to citizens or state institutions," it added.
The deputy head of the Transitional Military Council (TMC), General Mohamed Hamdan Dagalo, warned of "vandals" and a "concealed agenda" that he suggested might seek to take advantage of the march.
Direct talks between the council and the FFC stalled and then collapsed altogether when security forces stormed a protest sit-in in central Khartoum on June 3, killing dozens.
The sit-in had become the focal point of protests against Bashir and the military council.
Mediators led by the African Union (AU) and Ethiopian Prime Minister Abiy Ahmed have since been trying to broker a return to direct talks between the two sides.
On Friday, the military council said a proposal submitted by the AU and Ethiopia received on June 27 was suitable for the resumption of talks with the opposition.
The opposition had supported an earlier Ethiopian proposal before the military council said the AU and Ethiopian efforts needed to be merged.
Separately on Saturday, the Sudanese Professionals' Association (SPA) said the head of a teachers' committee and a leading member of the FFC had been detained.
The military council did not immediately comment.
"We urge the international community to demand their immediate release. This move by the TMC is highly detrimental to confidence building at this crucial time," said the SPA, which is part of the FFC and spearheaded the anti-Bashir protests.The European Union on Friday said the Sudanese people's right to protest and express their views "is key" and supported the AU-Ethiopian mediation efforts.