The attackers, many of them carrying traditional weapons attacked Kinigi sector in Musanze district, a tourist hub where visitors visit the park to view the gorillas, an endangered species.
“Those criminals killed eight people including six who were killed using traditional weapons and two who were shot dead. 18 people were injured and are being attended by doctors,” police spokesman John Bosco Kabera said in a statement.
Security personnel were searching for the attackers, he said.
Police did not say whether any tourists were among those killed. However, the hotels in the area are heavily guarded by the military and are unlikely to have been attacked.
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It was not clear who the attackers were or where they came from but Rwanda has in the past seen incursions by fighters from the rebel FDLR force from their bases in eastern Democratic Republic of Congo.
The FDLR is composed of former Rwandan soldiers and Hutu militias who fled after taking part in the 1994 genocide in Rwanda.
Over the years various groups opposed to Rwanda have found sanctuary in DRC’s vast eastern jungles from where they have occasionally launched attacks on the country.