It said the fighting was continuing Monday in Fizi, a region of South Kivu, a mineral-rich province which is prone to ethnic tensions.
The unrest is another front in the push by rebels to oust President Joseph Kabila as the poverty-stricken Democratic Republic of Congo limps towards a much-delayed presidential election slated for December 23.
"Three soldiers drowned in a river with their weapons," he added.
The clashes pit the army against rebels loyal to a former army general, William Amuri Yakutumba, opposed to Kabila.
The militia is allied to rebels of the National Liberation Front based in neighbouring Burundi, according to several regional sources.
In February the military said they had wiped out the Yakutumba with help from Burundi, where some of them had taken refuge.
The Fizi region was the cradle of the rebellion by Laurent-Desire Kabila, father of the current president, who ousted Mobutu Sese Seko in May 1997.
The former Belgian colony has not seen a peaceful transition of power since 1960.
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