Goma — Fighting broke out on Friday between M23 rebels and the Congolese army.
The clashes, the first in two months, come after the collapse of peace talks in Kampala between the M23 and the Democratic Republic of Congo (DRC) government.
General Sultani Makenga, M23's commander told Reuters: "They attacked us. We are going to defend our positions."
M23 and the DRC government had for three months been in peace talks under the mediation of Uganda.
The talks collapsed over disagreement on amnesty for the rebels and their reintegration into the Congolese army.
The Congolese army accused the rebels of attacking their positions in the Friday fighting. But on Saturday M23 said their positions were attacked by the Congolese army.
DRC army spokesman, Olivier Hamuli said the M23 had been forced out of Kibumba, a town hear Goma where fighting has been taking place.
"We have pushed M23 into the hills on the Rwandan border," Oliver Hamuli told Reuters. "We now call on Rwanda to help us disarm their fighters."
Rwanda has said mortar shells from the fighting fell into her territory.
Rwanda has been accused by the United Nations group of experts and the DRC government of supporting the rebels but Kigali denies the accusations.
The M23 is largely made up of Tutsi rebels who were previously part of the Congolese army, but mutinied in April 2012 when they accused the DRC government of not respecting a 2009 peace deal.
The UN has a 3,000 strong intervention brigade in DRC with a mandate to use force has been deployed. The force has fought the M23 rebels alongside the Congolese national army.