Two government soldiers also were killed in the clashes in the village of Kibumba, about 19 miles north of the regional capital of Goma, the BBC reported Friday.
North Kivu province Gov. Julien Paluku said rebels have claimed to be on the verge of capturing Goma but the city would not fall.
Thousands of people have fled the region because of the fighting, Paluku said.
The clashes are the worst since July, observers said.
Rwanda and Uganda have denied U.N. allegations that they are backing the rebels, also known as the Congolese Revolutionary Army.
M23 is comprised of soldiers who mutinied from the DR Congo army in April.
An estimated 500,000 people have been displaced since fighting began.
Notable deaths of 2014 [PHOTOS]