The head office of the Greater Nile Petroleum Operating Company in Khartoum was reduced to a smoldering wreck on Saturday as the RSF and SAF fought in the area.
One of the country's costliest buildings, the oil company's 18-story tower was built during an oil boom before South Sudan declared independence in 2011.
The RSF said SAF has targeted the building, along with other important buildings in an effort to dislodge paramilitary fighters from positions they captured across the capital early in the conflict.
Despite the RSF claims the army is responsible, it is unclear what caused the fire that burned through the tower.
There was no immediate comment from SAF.
The conflict between Sudan's rival forces broke out in mid-April when tensions linked to an internationally backed plan for a political transition boiled over.
The conflict has caused widespread clashes, looting and shortages of food and medicine in Khartoum and other cities, driving more than 5 million people from their homes.