South Sudan army spokesman Brig Malaak Ayuen said dozens were also wounded in the clashes in the state of Jonglei.
The local authorities accuse the government in Khartoum of backing the rebels to destabilise South Sudan, which will soon become independent.
The UN says more than 800 people have been killed in the region this year.
There are at least seven rebel groups operating in South Sudan.
Brig Ayuen said rebels led by Maj-Gen Gabriel Tang were responsible for the fighting on Saturday, south of the town of Malakal.
Gen Tang led a southern border militia allied to the government in Khartoum during Sudan’s 21-year civil war that ended in 2005.
His forces were accused of burning and looting southern villages along the Nile River during the conflict, which left two million people dead.
Members of the Sudanese armed forces loyal to Gen Tang in Malakal clashed with the Sudan People’s Liberation Army (SPLA) in 2006 and 2009 in breach of the peace deal. The 2006 fighting killed about 150 people.
He was pardoned by South Sudan’s president ahead of January’s referendum, in which southerners voted to secede. He also agreed to reintegrate his militia into South Sudan’s army.
In a separate incident in Jonglei, a Sudanese employee of the UN World Food Programme was killed on Friday by unknown assailants.
This week there have also been clashes in neighbouring Unity state, where a militia led by former SPLA Gen Peter Gadet began an assault on government forces, leaving at least 45 people dead.