Crowds of people - many of whom had taken refuge in the city from violence in the capital Khartoum - could be seen packing up their belongings and leaving on foot in video posted on social media on Saturday.
"The war has followed us to Madani so I am looking for a bus so me and my family can flee," 45-year-old Ahmed Salih told Reuters by phone.
"We are living in hell and there is no one to help us."
The central city of Wad Madani is the new front of the war in Sudan with thousands fleeing. (AP PHOTO)
Sudan's army, which has held the city since the start of the conflict, launched air strikes on RSF forces to the east of the city, the capital of Gezira state, as it tried to push back the assault that started on Friday, witnesses said.
The RSF responded with artillery and RSF reinforcements were seen moving in the direction of the fighting, the witnesses added.
RSF soldiers have also been seen in villages to the north and west of the city in recent days and weeks, residents said.
The United Nations said 14,000 people had fled the area so far, and a few thousand had already reached other cities. Half a million people had sought refuge in Gezira, mainly from Khartoum.
The fighting has raised fears for other army-held cities in southern and eastern Sudan where tens of thousands of people have been sheltering.
"I urge the RSF to refrain from attacks and for all parties to protect civilians at all costs. Perpetrators of terror will be held accountable," the US Ambassador to the UN, Linda Thomas-Greenfield, said.
The army and RSF last week cast doubt on an East African mediation initiative aimed at ending a war that has triggered the largest internal displacement in the world and warnings of famine-like conditions.
In Khartoum and cities in Darfur that the RSF has already taken, residents have reported rapes, looting and arbitrary killing and detention. The group is also accused of ethnic killings in West Darfur.
The RSF has denied those accusations and said anyone in its forces found to be involved in such crimes would be held accountable.
Sudan's army has been doing battle with the paramilitary Rapid Support Forces for eight months. (AP PHOTO)
On another front, activists reported fresh clashes after weeks of relative calm around the city of El Fasher, the capital of North Darfur state.
RSF forces surrounding that city had earlier stopped their advance there after other armed groups said they would get involved.
Residents also reported heavy strikes by the army in Nyala, South Darfur, and in Bahri, one of the cities that make up the wider national capital with Khartoum.
While the army has not made a statement on the fighting in Wad Madani, Sudan's foreign ministry branded the RSF as terrorists for a "declared attack on a number of safe villages and neighbourhoods (in the) east of Gezira state which are devoid of military targets".
The war between the RSF and the Sudanese army broke out in April after disputes over a transition to democracy and integration of the two forces.
