The RSF seized control of the camp on Sunday after a four-day assault that the government and aid groups have said left hundreds dead or wounded.
Rights groups have long warned of possible atrocities should the RSF succeed in its months-long siege of the famine-stricken camp, neighbour to the army's only remaining stronghold in the Darfur region, al-Fashir.
Satellite imagery from Maxar Technologies showed burning buildings and smoke in Zamzam on Friday, echoing prior RSF attacks.
The RSF has dismissed such allegations, and says the Zamzam camp was being used as a base for army-aligned groups.
At the start of the war, the camp was home to about half a million people, a number that is thought to have doubled.
In a video shared by the paramilitary force, RSF second in command Abdelrahim Dagalo is seen speaking to a small group of displaced people, promising them food, water, medical care and to be able to return to their homes.
The RSF accelerated its assault on the camp after the army regained control of the capital Khartoum, cementing its re-taking of the centre of the country.
It has also accelerated drone attacks into army-controlled territory, including an attack on the Atbara power station in the north of the country on Monday according to the national electricity company, cutting off power to the wartime capital of Port Sudan.
The war in Sudan erupted in April 2023, sparked by a power struggle between the army and the RSF, shattering hopes for a transition to civilian rule. The conflict has since displaced millions and devastated wide swathes of the country, spreading famine in several locations.
