Clashes were under way between the M23 and a Hutu militia in Bambo, 70 kilometer north of the provincial capital Goma, local sources told AFP by telephone.
"Heavy weapons fire can be heard, people are in a panic," a civil society representative said.
A security source confirmed the firing between the M23 and combatants from the Democratic Forces for the Liberation Rwanda (FDLR), a Hutu faction present in the DRC since the Tutsi genocide in 1994.
During the morning, fighting was also reported near Bwiza, close to the former stronghold of ex-Tutsi rebel leader Laurent Nkunda, who operated there in the noughties.
DRC's President Felix Tshisekedi and Rwandan Foreign Minister Vincent Biruta attended a mini-summit in the Angola on Wednesday, which concluded with a deal on the cessation of hostilities in eastern DRC from Friday evening.
M23 rebels were then to withdraw from "occupied zones".
But the rebels, a largely DRC Tutsi militia, said Thursday the ceasefire "doesn't really concern us", and called for "direct dialogue" with DRC's government.
The rebels have recently seized swaths of territory north of Goma, a city of one million which they briefly captured 10 years ago.
Kinshasa has refused to engage with the M23, which it calls a "terrorist movement", as long as it occupies territory in the DRC.
The M23 is among scores of armed groups that have turned eastern DRC into one of Africa's most violent regions.
Many are legacies of two wars before the turn of the century that sucked in countries from the region and left millions dead.
