Fighting between the M23 and opposing armed groups broke out in the Tongo area of North Kivu's Rutshuru territory on Thursday, according to locals and militia members.
Safari Haguma, a local civil society figure, told AFP via telephone that heavy gunfire had been heard since that morning.
Dominique Ndaruhutse, the self-proclaimed general of the CMC/FDP militia, also confirmed the clashes and said 13 members of the M23 had been killed.
AFP was unable to independently confirm the death toll.
"We took up arms to defend the territorial integrity of our country and we will never accept being slaves," said Jules Mulumba, a spokesman for a coalition of armed groups that includes the CMC/FDP.
He added that he thought the M23 aimed to advance towards the town of Kitshanga, which lies about 125 kilometers to the west of Goma, in a bid to cut off the city.
An assortment of armed groups -- of which there are more than 120 in eastern DRC -- have lately led the fight against the M23.
The DRC has accused its smaller central African neighbor Rwanda of backing the M23, which Kigali denies.
But the United States and France, among other Western countries as well as United Nations experts, agree with the DRC's assessment.
Under heavy international pressure to cease fighting, the M23 delivered the strategic town of Kibumba to a regional military force last week, calling the move a "goodwill gesture done in the name of peace".
But the Congolese army dismissed the withdrawal as a "sham" aimed at reinforcing the group's positions elsewhere.