At least five Congolese soldiers have been killed by the Rwandan army, the Congolese military says.
Gen Bruno Mandevu said the clash occurred in the famous Virunga National Park, on Congolese territory – a claim Rwanda denied.
He said the Congolese troops initially thought they were fighting one of the many rebel groups active in the area.
A Rwandan army spokesman told the BBC that it was Congolese troops who had crossed the border.
Rwanda has twice invaded its much larger neighbour, sparking decades of conflict.
Eastern Democratic Republic of Congo, across the border with Rwanda, remains deeply unstable.