Sudan's army had warned Thursday of a possible confrontation between the two forces following mobilization by the RSF.
The RSF, which together with the army overthrew long-ruling autocrat Omar al-Bashir in 2019, began redeploying units in the capital Khartoum and elsewhere amid talks last month on its integration into the military under a transition plan leading to new elections.
RSF chief Dagalo, better known in Sudan as Hemedti, has been deputy leader of the ruling Sovereign Council headed by army chief General Abdel Fattah al-Burhan since 2019.
Sources close to both men said on Friday that they still remain at odds over who would be the commander-in-chief of the military during a multi-year integration period. The RSF says it should be led by the civilian head of state, a situation the army rejects.
That dispute has delayed the signing of a final agreement with political parties and the formation of a civilian government.
Following Thursday's warning from the army, several local and international players stepped forward with offers of mediation, including Finance Minister Jibril Ibrahim, Darfur Governor Minni Minawi and Sovereign Council member Malik Agar, three former rebel leaders who received posts following a 2020 peace deal.
"After an honest and serious conversation, [Dagalo] assured us of his total commitment to not escalate, and his readiness to sit with his brother the head of the Sovereign Council and his brothers in the armed forces at any time and without condition," a statement from the three men said.
Army sources told Reuters that in order to de-escalate, the RSF needed to withdraw its forces from near a military airport in the northern city of Merowe, and that its movements needed to happen in coordination with the military and within legal limits. RSF sources told Reuters on Friday that the movements had occurred in coordination with Burhan.