Khartoum accuses South Sudan of backing the insurgents, a charge which the government in Juba denies.
The fighting comes after Sudan and South Sudan last Tuesday resumed African Union-led talks in Ethiopia to resolve security and other crucial issues.
The African arch-enemies have been at loggerheads and came close to an all-out war this year over the disputed border and oil revenues.
South Sudan seceded from Sudan in July 2011 with two-thirds of the region’s oil, while processing facilities and the pipelines were in the possession of Sudan.
The new oil-rich nation is one of the least developed countries in the world, with one in every seven children dying before the age of five.
Dozens of people have been reportedly killed in Sudan as rebels and government troops clashed on two fronts.
According to the army, at least 32 insurgents were killed during clashes in a village in the western Darfur region on Thursday. The rebels claim they drove government troops out.
Separately, the army claimed that 45 rebels were also killed in a village in South Kordofan, near South Sudan's border.
However, Rebels of the Justice and Equality Movement (JEM) from Darfur, in Sudan's west, said they and other insurgents liberated the village, in the East Jebel Marra Mountains, killing at least one soldier.
Casualty claims are difficult to verify with access to both Darfur and South Kordofan restricted.
Last year, JEM insurgents formed an alliance with the rebels of the Sudan People's Liberation Movement-North (SPLM-N) with the aim of toppling the government of President Omar al-Bashir.