Machine gunfire broke out at dawn along the border after what the Congolese army said was the abduction of one of their soldiers by Rwandan troops who had crossed the border into the restive province of North Kivu.
The skirmishes later escalated, with Congolese military officials saying the sides had traded heavy weapons fire while locals reported "mortars and even rockets" being used through the afternoon.
A DR Congo government spokesman confirmed the abducted corporal had been killed and blamed Rwandan troops.
"On Wednesday ... A section of the DRC army crossed the border to Rwanda where they opened fired on a Rwanda Defence Force (RDF) patrol," the government said in a statement.
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"The attacks in the morning were followed by a second attempt: a deployment of two FARDC (Congolese) platoons to Rwanda, which led to a new firefight that killed four FARDC soldiers."
Rwandan Foreign Minister Louise Mushikiwabo said the country stood "ready to act to protect its citizens" against further attacks.
"We are in contact with both governments and are trying to understand exactly what happened... This is to reduce the tension," a senior United Nations official told AFP.
The violence -- the most severe to break out between the two neighbours since the end of last October -- could undermine international efforts to bring stability to Congo's mineral-rich but lawless east after years of bloody conflict.
Kigali and Kinshasa have long been at odds, with Rwanda repeatedly accused by the United Nations and its neighbour of backing the M23 rebels in the strife-torn Democratic Republic of Congo.