Human Rights Watch said it spoke with more than 50 people, including members of the armed group in detention, local government officials and 32 witnesses to the killings, which took place between Dec. 30 and Jan. 3 in the province of Cibitoke.
There was no immediate comment from the Burundian government.
Although there is limited information about the armed group, it appears members crossed into Burundi from neighboring Congo in late December, the rights groups said.
"The Burundian security forces have a responsibility to defend citizens against violence, but that cannot mean murdering those they have detained," said Daniel Bekele, Africa director at Human Rights Watch.
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"It appears that members of the military and police made no effort to arrest most of the men who surrendered, shooting them dead instead.
Bekele said that the involvement of police, military, and local government officials, as well as youth from the ruling party, shows coordination in the executions and state complicity.
Burundi's government has said fighting with the rebels led to the death of 97 combatants including two soldiers.