Images posted online showed a section of the bridge about halfway across the river had disappeared. Photo courtesy Sudan War Monitor
Since April, forces loyal to army chief Abdel Fattah al-Burhan have been at war with the paramilitary Rapid Support Forces (RSF) commanded by his former deputy, Mohamed Hamdan Daglo.
Witnesses reported "clear signs of destruction on the Shambat Bridge" which crosses the White Nile and connecting Khartoum's sister cities of Khartoum North and Omdurman.
Images posted online, which AFP was unable to immediately verify, showed a section of the bridge about halfway across the river had disappeared. Vehicles, apparently damaged, lay on the part of the bridge still standing.
The army said in a statement that "the rebel militia destroyed the Shambat Bridge early this morning... adding a new crime to their record."
The paramilitary force denied the accusation.
In August, airstrikes and artillery fire launched by army forces loyal to Burhan hit the Shambat Bridge.
Their paramilitary rivals had used the bridge as a supply route, a local resident and a military expert told AFP.
Intense fighting took place over the week in Khartoum and its surrounding areas, as well as the vast western region of Darfur, where some of the bloodiest clashes have taken place.
On Thursday, witnesses told AFP that corpses in military uniforms lined the streets of a district of Khartoum, while a shell hit Al-Nau hospital in the north of Omdurman, the last operational medical facility in the area, killing an employee.
North of the Sudanese capital Khartoum on Tuesday, a massive fire ignited at an RSF-controlled oil refinery which the paramilitaries blamed on an army air strike, though the army said "a fuel tanker belonging to the militia exploded".
This comes as Sudan's warring parties failed to negotiate a ceasefire during the latest talks held this week in Saudi Arabia.
The UN warned Friday of soaring human rights violations in Sudan's Darfur region, where the RSF has claimed control of all but one major city.
"We continue to receive unrelenting and appalling reports of sexual and gender-based violence, enforced disappearance, arbitrary detentions and grave violations of human and children's rights," said Clementine Nkweta-Salami, the UN humanitarian coordinator for Sudan.
Since fighting broke out on April 15, more than 10,000 people have been killed in Sudan, according to a conservative estimate from the Armed Conflict Location & Event Data project.
About six million people have been uprooted from their homes, according to UN figures.