Fighting from Friday to yesterday between police and troops on the one hand and members of a local militia on the other left "13 dead and 14 injured among security forces" and "18 dead" militia fighters, Hubert Mbingho N'Vula said on state television.
"Public order has been restored," he said.
Earlier in the day he had given the militia toll as just 10 fighters.
The fighting was due to rivalry between the newly named traditional chief and his uncle, "who came to oust his nephew and seize power", an interior ministry official told AFP.
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Fighting between the militia and government forces lasted throughout Saturday night and a large part of yesterday.
Kasai is a particularly isolated and under-developed region in DR Congo.
DR Congo has been wracked by recent violence sparked by a political crisis brought on by the postponing of a presidential election which had been due to take place before the end of the year.