The takeover could be a turning point in the Rapid Support Forces' (RSF) advance through western and central regions of Sudan.
Its approach on Wad Madani, southeast of the capital Khartoum, since Friday has caused thousands of people to flee.
The city lies in Gezira State, an important agricultural region in a country facing worsening hunger.
There was no comment from the army.
The two forces had shared power with civilians after the 2019 overthrow of former strongman Omar al-Bashir before staging a coup together in 2021 then coming to blows over an internationally backed political transition plan.
Videos posted by the RSF showed fighters in pick-up trucks driving along streets in Wad Madani and over a bridge across the Blue Nile that it had been fighting over with the army.
Witnesses said they also raided nearby villages.
In one video, RSF fighters carrying rifles stood with their arms around Coptic priests, who said they had not been able to flee but asked the RSF for help leaving the city.
The videos were not verified by Reuters.
Some residents of Khartoum had fled the Sudanese capital for Wad Madani to escape fighting. (AP PHOTO)
Local pro-democracy activists said that the RSF had set up checkpoints throughout the city and were looting homes and cars, while the army and police were not seen.
The war between the army and the RSF has forced more than seven million people to flee their homes, left the capital in ruins, caused a humanitarian crisis and triggered waves of ethnically driven killings in Darfur.
In Khartoum, the RSF has been accused of looting homes, raping women and arbitrary killings and detentions.
While half a million had sought refuge in the wider Gezira state, at least 85,000 were living inside Wad Madani, with more relying on the city for healthcare, aid and government services which began shutting down in recent days.
Pro-democracy group Emergency Lawyers said the RSF on Monday killed two people when it raided Rufaa hospital to the north of Wad Madani.
"Fleeing again will completely deplete our resources," said Heba Abdelrahim, who had come to Wad Madani with her family from Khartoum.
"Thinking logically we will wait until we don't have any other choice."
Several neighbouring families had left together on a large truck, she said.
Abdelrahim said gunshots could be heard while army warplanes were flying overhead, with air strikes heard before sundown.
The United States, which on Sunday urged the RSF not to attack Wad Madani, and Saudi Arabia have led mediation efforts which have so far been fruitless.
While regional mediators IGAD said the army and RSF agreed to a ceasefire last week, both sides quickly backed out.
Taking control of central Wad Madani, a hub for Sudan's highways, gives the RSF greater control of trade and allows it to hobble the army's supply routes, said researcher Reem Abbas, a fellow at the Tahrir Institue.
"This gives them time to organise themselves, and they can start going east... They will continue to hold people hostage, putting pressure on the communities, on the army and the international community," she said.
The RSF said in a statement it sought to oust Bashir loyalists in Wad Madani and pre-empt an attack by the army, which it accused of racial killings and indiscriminate air strikes.
Emergency Lawyers in separate statements criticised killings and torture on a racial basis that happened in Gezira state, and said at least 10 people had been killed by air strikes in RSF-controlled Nyala in recent days.
