The conflict has caused a devastating humanitarian crisis, and clashes have killed nearly 16,000 people and displaced millions.
The district, filled with Sudanese shops and restaurants, is a magnet for the growing numbers of people who have fled Sudan or find themselves unable to return because of safety fears.
The Sudanese army announced its successful defence, citing the destruction of RSF vehicles, the seizure of two tanks, and the elimination of dozens of RSF members.
The conflict, now in its tenth month, has seen dynamic changes, with the SAF on the verge of breaking the RSF siege on the Engineers Corps in Omdurman.
The UN food agency said Friday it has received reports of people dying from starvation in Sudan.
An estimated 9.05 million people have been internally displaced in Sudan from the internal conflict.
Khartoum declared on Tuesday the suspension of its engagement and the freezing of all interactions with the Intergovernmental Authority on Development (IGAD) concerning the ongoing conflict in the country.
On Wednesday, Sudan's largest fuel production facility, the Khartoum oil refinery in AlJaili, was engulfed in flames, triggering accusations between the Sudanese Armed Forces (SAF) and Rapid Support Forces (RSF) over its cause.