RSF troops attacked and looted the vast Abu Shouk camp on Wednesday, killing an unknown number of people and wounding at least 13, locals said, more than a year into Sudan's conflict.
Around 60% of the more than 100,000 inhabitants fled on Thursday, according to the Coordinating Committee for Refugees and Displaced People, which oversees camps in the region.
Fighting continued in other parts of El-Fasher on Friday, locals said.
The RSF and its allies swept through four other Darfur state capitals last year and were blamed for a campaign of ethnically driven killings against non-Arab groups and other abuses in West Darfur - accusations denied by the paramilitary group.
There was no immediate comment from the RSF or the Sudanese Armed Forces, SAF, on the latest clashes in El-Fasher, a historic center of power.
The rival forces have blamed each other for the violence.
The U.N. special adviser on the prevention of genocide this week said there was a risk of genocide, and allegations that it was already taking place.
Civilians in El-Fasher and other parts of Darfur were being targeted based on their identity and skin color, Alice Wairimu Nderitu told the U.N. Security Council on Tuesday.
Abu Shouk is home to survivors of the violence in Darfur two decades ago, where Janjaweed militias, the precursors to the RSF, fought alongside the Sudanese army and were accused of genocide.
About half a million more people moved into El-Fasher during the ongoing war that broke out between SAF and the RSF in the capital Khartoum in April 2023, as long-simmering tensions over integrating the two forces came to a head.
At least 85 people have died at the only functioning hospital in the south of El-Fasher since May 10, according to medical charity Médecins Sans Frontières, MSF.
The total number of casualties is much larger as civilians hit by fighting in the north, east, and south of the city have not been able to reach medics, MSF and residents say.
The RSF has accused the army of using human shields as well as carrying out extensive air strikes, including destroying El-Fasher's power station.
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