Congolese regional commander Colonel Ephrem Ramazani said there had been "heavy weapon fire from both sides" as clashes erupted after several hours of calm.
Gunfire broke out today after Rwandan troops crossed the border into the restive province of North Kivu and abducted a Congolese soldier, according to a local army spokesman who gave no details on casualties or the fate of the soldier.
A local from a village near the fighting said the troops had used "mortars and even rockets" in the fighting, which re-started around 2:00 pm and continued into the afternoon.
Rwanda last year accused the Congolese army of firing rockets and mortar shells on its territory and massed troops along its border in response, sparking fears the decades-long conflict between the two nations could reignite.
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Rwanda fought against the central government in Kinshasa in Congo's two wars in 1996-97 and 1998-2003 and has been involved in several attempts to destabilise the country, backing uprisings by Tutsi-dominated militias.
But since the defeat in November of a Kigali-backed rebellion led by the M23 group, the border has remained relatively calm.
"There was shooting between elements from the Rwandan army and the FARDC (the Congolese army) in Kanyesheza," he told AFP.
The fresh violence could undermine international efforts to bring stability to Congo's mineral-rich but lawless east after years of bloody conflict.
Last year the Great Lakes regional body set up the Joint Verification Mechanism (JVM) -- a multinational team of military officers -- to defuse the M23 crisis.
A source at the JVM said a monitoring mission sent to assess the fighting at Rwanda's request was forced to turn back to Goma "due to tension in the area" and would remain there until the situation had calmed down.