Government troops and rebel forces engaged in serious fighting in the oil-producing Upper Nile state yesterday, military spokesman Brig Philip Aguer told The Associated Press.
Fourteen government soldiers were killed and 17 others wounded in fighting in Manyo County, he said.
After the rebels were dislodged from their positions, some fled toward Sudanese territory, he said.
"Following heavy fighting there, the (South Sudanese military) is now in control of Manyo County in Upper Nile state, particularly the area of Gabat, where the rebels used to approach and shell the town of Renk from the western side of the Nile River," he said.
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It was not immediately possible to get a comment from the rebels.
South Sudan has seen violence since December 2013, when government troops in the capital, Juba, splintered and fought along ethnic lines.
Several peace talks have failed despite international pressure for a political deal between Kiir and Riek Machar, the former deputy president who now commands rebel forces.
It is widely believed the current conflict was fuelled by a power struggle between Kiir and Machar, who was fired in July 2013.
On Sunday at least 70 people were killed in clashes in South Sudan's central region.
Forty-one men from Rumbek Centre County in Lakes state and 37 from neighbouring Rumbek North were killed when militia from the rival counties clashed over grazing land, Mawat Manuer, commissioner of Rumbek Centre said today. The Rumbek North raiders stole 2,165 cows, he said.