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The army has managed to hold on to El Fasher but tension has been mounting as the RSF has been besieging the city since the middle of last month and threatening an assault.
Since Friday, residents have witnessed intense clashes and the exchange of heavy mortar fire, a freelance journalist in the city told the BBC.
At some point overnight into Sunday a blast in front of the MSF-supported Babiker Nahar Paediatric Hospital in El Fasher "led to the collapse of the roof above the intensive care unit and the death of two children receiving treatment there, as well as some caregivers", the charity said in a brief statement sent to the BBC.
Patients were also injured and those who could make it sought safety in another hospital, which had already taken in 160 wounded people on Friday.
It is not clear who was responsible for the attack.
The southern part of the city, once considered safer and a refuge for displaced people, has been under fire.
Fear now pervades El Fasher as residents are unsure where to seek refuge.
The UN's humanitarian co-ordinator for Sudan said that "the violence threatens the lives of over 800,000 civilians".
"It is heartbreaking to see this nightmare unfolding... This must stop," Clementine Nkweta-Salami said.
Sudan’s brutal civil war began in April last year, after the country’s two leading military men who had staged a coup together – one the head of the armed forces, the other the head of the RSF – fell out over the future of the country.
International efforts to broker a ceasefire have repeatedly failed.