According to media reports, those involved are ready to resume the dialogue in the Saudi city of Jeddah, where their representatives are still staying.
The mediators also asked to agree on a new cease-fire, effectively implemented, with the aim of building a permanent cessation of military operations.
The fighting in Sudan is nearing its second month without a secure and reliable peace agreement in sight.
The conflict has already left thousands of victims dead and wounded, and more than two million people displaced.
The clashes broke out last April 15 due to contradictions in the middle of a process of integration of the Rapid Support Forces, led by Mohamed Hamdan Dagalo, vice-president of the Sovereign Transitional Council (CST) within the Armed Forces, and the head of the Army and president of the CST, Abdelfatá al Burhan.
Both holding the rank of general, they have been vying for control of the country after the 2019 overthrow of President Omar al-Bashir.