After several days of relative calm, fighting erupted on Monday in the flashpoint province of North Kivu, leaving several civilians dead and injured, hospital sources and aid workers said.
The fighting continued on Tuesday, with the rebels seizing new villages, despite a ceasefire brokered by Angola last week that was due to start at noon.
The M23 rebels have captured swathes of territory in eastern Democratic Republic of Congo since re-emerging from dormancy in late 2021, claiming the government had ignored a pledge to integrate them into the army.
The Tutsi-led group is hemming in the lakeside trade hub of Goma, taking territory to the north of the city and advancing in the west as well.
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 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.
Despite the clashes, the M23 rebels in a statement on Tuesday announced what they called "an effective ceasefire" at midday "to open the way for direct dialogue with the Kinshasa government".
Both sides accuse the other of triggering the fresh round of clashes.
M23 spokesman Willy Ngoma told AFP on Tuesday that the group was defending itself after the army attacked all its positions simultaneously.
Lieutenant-Colonel Guillaume Ndjike, the army's spokesman in North Kivu, said late Monday the M23 "and their sponsors from the Rwanda Defence Force" had attacked a recently deployed Burundian contingent of an East African regional military force.
He said the rebel attack also targeted a camp for displaced people and the area of Mubambiro, 20 km west of Goma, causing "huge damage".
The DRC accuses Rwanda of backing the rebels, who have displaced over half a million people in their long campaign.
Independent UN experts, the United States, as well as several other western states, agree with the assessment, although Rwanda strongly denies it.
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.
Another civil society representative, Leopold Muisha from the Kamuronza district on the western outskirts of Goma, said rebels had shelled civilians.
"Seven bombs were fired on Monday in the late afternoon, killing two civilians, including a 12-year-old child, and injuring six others," he said in a statement.
The International Committee of the Red Cross (ICRC) also reported one dead and seven injured in the bombardment.
On March 3, the Angolan presidency, which is mediating the conflict, announced a ceasefire for eastern DRC due to take effect at noon on Tuesday (1000 GMT).
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.
The seven-nation East African Community (EAC) has created a military force to stabilise eastern Congo, with the first troops arriving in Goma in November.
The announcement followed several other failed regional peace initiatives.