Violence has racked Sudan's border regions with South Sudan since around the time the southern nation seceded a year ago under a 2005 peace deal that ended decades of civil war.
Hundreds of thousands of people have fled their homes in South Kordofan and nearby Blue Nile state since the fighting broke out, the United Nations has said, Reuters reports.
Aid groups have warned of a large scale humanitarian disaster in the two states as food stocks dwindle - something Khartoum denies.
Rebels from the Sudan People's Liberation Movement-North (SPLM-N) said they "liberated" El Faragil, a village west of Delling - one of the largest towns in South Kordofan - on Wednesday.
In a statement, the insurgents said they inflicted "heavy losses" on government forces and captured weapons and other military equipment.
Sudan's armed forces spokesman, Al-Sawarmi Khalid, said the rebels had actually lost the battle.
"What happened was that our forces defeated the (SPLM-N) forces and evicted them from the mountains in the El Faragil area," he said, adding the clashes had taken place over the last two days.
Both sides often make conflicting statements which are difficult to verify independently because of the remoteness of the region and limits on access.
The SPLM-N fighters in South Kordofan are among tens of thousands who sided with the South against Khartoum during Sudan's civil war, but were left north of the border under the peace pact.
Last year, the insurgents formed an alliance with other rebels in Sudan's western Darfur region with the aim of toppling the government of President Omar Hassan al-Bashir.
The rebels say their border regions have been left underdeveloped and marginalised by an Arab elite in Khartoum. Khartoum has said it is determined to restore order to the territories and accuses its old foe South Sudan of backing the insurgents.
Khartoum and Juba have traded accusations over support for rebels on one another's territory, complicating already-fraught talks over an array of unresolved partition-related issues.
The two countries were expected to resume African Union-brokered security talks in Addis Ababa on Thursday.
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