A spokesman for the rebels, Vianney Kazarama, said they were leading the attack in Kirolirwe to take weapons from the army.
He said elements from a former rebel group in Congo, the National Congress for the Defence of the people - known as CNDP - backed the attack.
The fighting lasted all day and moved towards Sake, a town near Goma, the capital of North Kivu province. The M23 has threatened to take Goma, but has not launched any attacks there so far.
Congolese army spokesman Olivier Hamuli said the army pushed the rebels back into the Virunga National Park, home to some of the last mountain gorillas. He said they were bombing that area.
On Friday, the UN security council said it intended to impose sanctions on the M23 rebels and others who were violating the arms embargo in Congo.
"The security council strongly condemns the M23 and all its attacks on the civilian population, United Nations peacekeepers and humanitarian actors, as well as its abuses of human rights, including summary executions, sexual and gender based violence and large scale recruitment and use of child soldiers," the statement said.
"The security council also condemns the attempts by the M23 to establish a parallel administration and to undermine State authority."
The council also alluded to allegations that Rwanda and Uganda are supporting the rebellion, calling on neighbouring nations to avoid interfering.
The M23 rebel group of about 1000 fighters was created after several officers from the Congolese army defected in April and May and launched a rebellion to demand better pay, better armaments and amnesty from war crimes.
The group has a stronghold now on the border with Uganda and Rwanda, which has helped fuel allegations that Uganda and Rwanda are backing the rebellion as arms can be easily smuggled into their territory.
On Tuesday, a leaked UN report accused both Uganda and Rwanda of supporting the rebellion, which both countries strongly deny.
Congo's mineral-rich east is facing the worst upsurge in fighting in years, with at least 320,000 people forced from their homes, according to the UN.
The conflict is a spillover from the 1994 Rwanda genocide. Hundreds who participated in the mass slaughter escaped into Congo and still fight there.
The M23 rebels are an incarnation of a group of Congolese Tutsi set up to fight Rwandan Hutu rebels in Congo.
