Black smoke rose Sunday from a famous glass-fronted skyscraper, the 18-story Greater Nile Petroleum Company Tower.
Photos and videos published by local media showed other towers housing the Justice Ministry and the tax authority on fire.
In a statement on Monday, the Foreign Ministry, which is controlled by Sudan's military, accused the paramilitary Rapid Support Forces of "targeting a number of major and important economic institutions and commercial buildings in the country" over the past two days.
Earlier, the RSF blamed the Sudanese Armed Forces for carrying out "attacks in Khartoum", which it said "affected vital facilities".
Aerial bombardment has escalated since fighting broke out in mid-April between Sudan's army and the Rapid Support Forces (RSF).
Some of these airstrikes hit populated areas, resulting in numerous civilian casualties.