The rebels said they had repulsed a government attack
The Sudanese military has launched an air and ground assault on insurgents' positions in South Darfur, according to a rebel group.
The Justice and Equality Movement (Jem) said the attack had targeted the town of Muhajiriya, which war planes reportedly also bombed at the weekend.
Peacekeepers said explosions and war planes had also been heard around the the North Darfur capital of El Fasher.
Air attacks are forbidden in Sudan under the terms of a peace deal.
BBC Sudan correspondent Amber Henshaw says the reported fighting would mark an escalation in the ongoing Darfur conflict, almost six years after it began.
It comes as the International Criminal Court mulls whether to issue an arrest warrant for Sudan's President Omar al-Bashir on charges of orchestrating war crimes in Darfur.
There was no immediate comment from the army on reports of Monday's fighting.
Senior Jem official Tahir el-Faki told the BBC the government launched ground and air attacks at around midday at Muhajiriya, where reported air raids killed at least one person on Saturday.
He also said the government launched another military operation on Monday east of El Fasher.
Mr el-Faki added that Jem forces had earlier advanced on the town's airport, which he said was being used as a base for launching bombing raids, before halting.
United Nations African Union (Unamid) peacekeepers said they were gravely concerned.
The mission's spokesman, Noureddine Mezni, told Reuters news agency they had heard "explosions, shelling, mortars and sounds of fighter jets" near El Fasher, but had no details on who was fighting.
In May last year Jem attacked Omdurman, just across the River Nile from the capital Khartoum, taking parts of the city before being driven out by government forces.
The UN says up to 300,000 people in Darfur have died and more than 2.2 million have been displaced since the uprising against Sudan's Arab-dominated government started in February 2003.
Khartoum says just 10,000 have died. It says the scale of the suffering has been exaggerated for political reasons.