RSF said in a statement that it had taken control of the presidential palace and Khartoum's airport in response to the army's attacks. Flight data shows that planes turned around after almost landing at the airport.
Unrest has grown in the large African country this week after the army criticized RSF establishing a military presence in more places in the country.
It is about a split between the two parallel military powers that has developed in Sudan.
RSF (Rapid Support Forces) was formed from the Janjaweed militias, which the country's then leader Omar al-Bashir sent out to spread fear in Darfur in western Sudan in the 00s.
Since then, the force has operated in parallel with the army, and they collaborated on the coup that overthrew the country's democratically elected rule in October 2021.
But the latest split increases fears of a new civil war.