Battle hardened M23 rebels announced in a statement on Tuesday that they want a direct dialogue with the Kinshasa government.
The announcement was made after rebels called for “an effective ceasefire” at midday “to open the way for direct talks.
Fighting erupted on Monday and continued on Tuesday, with the rebels seizing new villages, despite a ceasefire brokered by Angola last week that was due to start at noon.
A security source, who declined to be named, said that Karuba, about 30 kilometres (18 miles) west of Goma, “has just fallen into rebel hands”.
“We attacked them in the night but this morning they launched a counter-attack, and, at the moment, the fighting is continuing,” the source added.
Witnesses said fighting continued to the north too, where rebels remained on the offensive.
The fighting in Karuba since Monday has killed six and left at least 10 injured, Folo Ombeni, deputy head of a local civil society group, said.
The renewed fighting coincided with an urgent appeal by UN chief Antonio Guterres on Monday for the M23 rebels to honour the ceasefire and move towards fully withdrawing from the conflict-ridden country.
M23 spokesman Willy Ngoma told press on Tuesday that the group was defending itself after the army attacked all its positions simultaneously.
During a visit to DR Congo last week, French President Emmanuel Macron met DRC President Felix Tshisekedi and his Angolan and Rwandan counterparts Joao Lourenco and Paul Kagame, saying all sides would support a ceasefire starting Tuesday.