Rwandan military officials say Hutu extremists based in eastern Congo crossed into Rwanda on Tuesday and launched attacks on villages near the border.
A military spokesman blamed the rebel Democratic Forces for the Liberation of Rwanda [FDLR] for the attack, which led to clashes with Rwandan military forces.
Reuters news agency reports the FDLR, which opposes Rwanda's Tutsi-led government, has denied involvement in any fighting.
Rwanda said the attackers, numbering at least 100, were repulsed and fled back into the DRC or elsewhere in Rwanda. It said six FDLR fighters were killed, two were captured, and that one civilian was killed.
Foreign Affairs Minister Louise Mushikiwabo said the attacks were an attempt to "take advantage of the volatile situation" in the border region and derail a regional peace process.
The attack took place a week after the Congolese rebel group M23 seized the city of Goma, near the Congolese-Rwandan border.
The M23 group, comprised mainly of Tutsi army defectors, defied a Monday deadline to withdraw from Goma that had been set by regional leaders.