Heavy fighting has been reported around the Presidential Palace and Army Headquarters in the capital Khartoum, witnesses told CNN.
A Reuters journalist saw cannon and armored vehicles deployed in streets, and heard the sound of heavy weapons fire near the headquarters of both the army and RSF.
In a statement, the RSF also claimed control of airports in Khartoum, Marwa and al-Abiad. Flights have been suspended inbound and outbound from the airport in Khartoum.
The RSF said they were responding to a surprise attack from the army on one of their bases.
The military has been in charge of Sudan since a coup in 2021, which ended a power sharing arrangement formed following the ousting of long-term former President Omar al-Bashir.
Talks have been under way on integrating the RSF into the army as part of the move towards the return of civilian rule, Reuters reports.
Additional reporting by Reuters.