The RSF said in a statement that it had taken full control of the camp belonging to the Central Reserve Police in southern Khartoum, and posted footage of its fighters inside the facility, some removing boxes of ammunition from a warehouse.
Reuters was not immediately able to verify the footage or the RSF statement.
There was no immediate comment from the army or the police.
Since late on Saturday, fighting has surged in the three cities that make up the wider capital – Khartoum, Bahri and Omdurman – as the conflict between the army and the RSF entered its 11th week.
Witnesses also reported a sharp increase in violence in recent days in Nyala, the largest city in the western Darfur region.
The United Nations raised the alarm on Saturday over ethnic targeting and the killing of people from the Masalit community in El Geneina in West Darfur.
Khartoum and El Geneina have been worst affected by the war although last week tensions and clashes escalated in other parts of Darfur and in Kordofan, in the south.
Fighting has intensified since a series of ceasefire deals agreed at talks led by the United States and Saudi Arabia in Jeddah failed to stick.
The talks were adjourned last week.
The Central Reserve Police has been deployed by the army in ground fighting in recent weeks.
It had previously been used as a combat force in several regions and to confront protesters demonstrating against a coup in 2021.
It was sanctioned last year by the United States, accused of using excessive force against protesters.
The army, led by Abdel Fattah al-Burhan, has been using air strikes and heavy artillery to try to dislodge the RSF led by Mohamed Hamdan Dagalo, known as Hemedti, from neighbourhoods across the capital.
“Since the early morning in north Omdurman we’ve had air strikes and artillery bombardment and RSF anti-aircraft fire,” 47-year-old resident Mohamed al-Samani told Reuters by phone.
“Where are the Jeddah talks, why did the world leave us to die alone in Burhan and Hemedti’s war?”
In Nyala, a city that grew rapidly as people were displaced during the earlier conflict that spread in Darfur after 2003, witnesses reported a marked deterioration in the security situation over the past few days, with violent clashes in residential neighbourhoods.
“Today I left Nyala because of the war. Yesterday there was bombardment in the streets and bullets going into homes,” Saleh Haroun, a 38-year-old resident of the city, told Reuters.
There was also fighting between the army and the RSF last week around El Fashir, capital of North Darfur, which the UN says is inaccessible to humanitarian workers.
In El Geneina, which has been almost entirely cut off from communications networks and aid supplies in recent weeks, attacks by Arab militias and the RSF have sent tens of thousands fleeing over the border to Chad.
On Saturday, UN Human Rights spokeswoman Ravina Shamdasani called for safe passage for people fleeing El Geneina and access for aid workers following reports of summary executions between the city and the border and “persistent hate speech” including calls to kill the Masalit or expel them.
Of those uprooted by the conflict in Sudan, nearly two million have been displaced internally and almost 600,000 have fled to neighbouring countries, according to the International Organisation for Migration.