Burundi is accusing Rwanda and the UN refugee agency, UNHCR, of holding Burundian refugees hostage.
In a statement on Wednesday, the government spokesman Philippe Nzobonariba urged neighbouring Rwanda to free and repatriate its citizens.
The statement followed deportation of some 2,500 Burundian refugees from Rwanda on Sunday and Monday.
The group, which belongs to a Catholic sect, refused biometric registration, a common practice under international laws on refugees, saying it would violate their religion.
Mr Nzobonariba urged the release of "other refugees taken hostage by the government of Rwanda in complicity with some agents of the Office of the United Nations High Commissioner for Refugees (UNHCR) in Rwanda."
Last week, 33 Burundian refugees, belonging to the group, were arrested in Rwanda for “instigating violence” during a registration exercise.
The group had left Democratic Republic of Congo in early March for Rwanda fearing deportation. They claimed they fled Burundi in 2015 due to religious persecution.