Residents reported "heavy artillery shelling" in the capital's northwest, while drones belonging to the paramilitary Rapid Support Forces attacked the air base north of Khartoum, witnesses told AFP.
The RSF said in a statement it had "destroyed three fighter jets, as well as stores of weapons, military equipment and supplies," adding that its forces had "killed or wounded dozens."
Since April 15, Sudanese army chief Abdel Fattah al-Burhan has been locked in conflict with his former deputy, RSF commander Mohamed Hamdan Dagalo.
The fighting — concentrated in Khartoum and the western region of Darfur — has killed more than 3,900 people and displaced more than 3.3 million.
An interior ministry statement said Thursday that a police lieutenant general had been killed in an attack on a police base earlier this month.
Police forces remain loyal to the army in the capital, but in war-ravaged region — where harrowing violence has brought accusations of war crimes — police have been seen fighting alongside the RSF.
Both sides have positioned themselves as guardians of democracy.
Burhan came to power, with Dagalo as his number two, in an October 2021 coup that derailed a fragile transition to civilian rule, before the two men fell out in a bitter feud.
On Thursday, the Forces for Freedom and Change — the main civilian bloc ousted in 2021 — denied links to the paramilitary, after one of the army's top commanders, Yasser Atta, this week referred to the civilian bloc and the RSF as "allies."
In a statement, the FFC called Atta's claims "misleading" and reiterated its "condemnation of all violations by both parties."