The army already controlled most of Omdurman, home to two big military bases. It appears intent on securing the entire capital area, which is made up of the three cities of Khartoum, Omdurman and Bahri, divided by branches of the River Nile. The RSF still holds territory in Omdurman.
Sudanese army chief Abdel Fattah al-Burhan, meanwhile, ruled out any reconciliation with the RSF in a video statement on Saturday in which he vowed to crush the group.
“We will not forgive, or compromise, or negotiate,” he said, reaffirming the military's commitment to restoring national unity and stability.
Burhan also said fighters who “repent to the truth” could still be amnestied if they lay down their arms, particularly those who are in rebel-held areas.
Earlier on Saturday, the army said it had taken control of a major market in Omdurman, which had previously been used by the RSF to launch attacks during a devastating two-year-old war.
The Sudanese army has also declared victory over the RSF in Khartoum, claiming control of most parts of the capital.