"They are fighting inside El Fasher town -- heavy fighting," one resident told AFP by telephone, adding that he could not identify the combatants, although some were in uniform.
Continuous gunfire was audible over the phone line as he spoke.
One source familiar with the incident said six militiamen were killed along with four government troops.
A medical source -- who asked not to be further identified -- said the bodies of four people were brought to hospital in the town.
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Government forces were trying to "flush out a militia" active in one of the town's neighbourhoods, a humanitarian source said.
"This is an area which has seen quite some criminality," including shooting around a UN warehouse, said the source, asking for anonymity.
The authorities apparently "decided that it was enough... and they needed to bring this part under control again".
Over the past two years, Sudan's deteriorating economy has led to worsening crime and intercommunal clashes in Darfur, a February report by UN chief Ban Ki-moon said, adding that some cash-poor paramilitaries had joined tribal militia fighting over gold and other resources.
"I heard the sound of heavy weapons," the resident said.
"I am in my house and I'm not going out to work."
Fighting had also been reported in El Fasher yesterday.