Yesterday's clashes pitched government troops against fighters from the Sudan Revolutionary Front (SRF), a coalition of three rebel groups, in the Dandur area 15 kilometres from Kadugli, Sudanese army spokesman Colonel Sawarmi Khaled Saad told AFP.
He said government forces had captured two T-55 tanks and killed 70 rebels.
But a spokesman for the Sudan People's Liberation Movement-North (SPLM-N), part of the SRF, denied Khartoum's version.
He said five rebels died in the fighting and that they had also shot down a Sudanese army helicopter.
South Sudan armed and trained the SPLM-N when it was part of the South's rebel force during the 1983-2005 civil war, but says it cut military ties before the South's independence in July 2011.
The SPLM-N says it is fighting Sudanese President Omar al-Bashir's government to put in place a government that respects the rights of the country's ethnic minorities.