Despite a peace deal in May, violence has increased in Sudan's remote west after rebels who rejected the accord formed a military alliance and renewed hostilities with the government.
Amnesty International said this month that 85,000 civilians have been unlawfully killed in fighting in Darfur.
Jar el-Neby, a Darfur rebel commander, told Reuters via satellite telephone: "The government troops and Janjawid militia attacked our positions and then attacked a village, killing five men and ... two women."
He said the government and their allied militia, known locally as Janjawid, attacked rebel positions near Kutum three days ago and the village of el-Goba, about 16km east of Kutum town on Friday.
Heavy clashes
In a separate statement, Esam el-Din Hajj, a Darfur rebel official, said his fighters had shot down two army helicopters during the clashes.
An army spokesman confirmed heavy fighting with the National Redemption Front (NRF), but denied that the attack on the village or that any aircraft had been shot down.
He said: "We did not use any helicopters or planes during the clashes so of course they could not shoot them down.
"Four soldiers were killed and around 20 to 25 injured."
Revolt
He also said that the rebels had attacked an army position in Shag al-Nakharah near Kutum.
He said the NRF had lost many troops and vehicles and eventually retreated.
Mostly non-Arab rebels took up arms in early 2003, accusing central government of marginalising the arid west.
World leaders say Khartoum armed militias to quell the revolt. Those militias stand accused of a campaign of rape, murder and pillage dubbed genocide by Washington.
Khartoum denies genocide but the International Criminal Court (ICC) is investigating alleged war crimes in the region.