In total, according to the latest information, around 37 people were killed (36 Burundian and one member of the armed forces) and between 117 and 134 people were injured.
Congolese police and soldiers opened fire as the migrants protested plans to send some of them home from the town of Kamanyola in the east of the country, activists say.
"No person who is a beneficiary of this (refugee) status is supposed to have an assault rifle".
Witnesses told AFP that numerous Burundians in Kamanyola were victims of religious persecution because they are followers of a female prophet called Zebiya, who has attested to seeing visions of the Virgin Mary in northern Burundi.
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The Congolese government, the U.N refugee agency and the U.N. peacekeeping mission in Congo "have deployed teams on site to shed light on everything that happened", said the coordinator of the U.N. Communications Group in Congo, Florence Marchal.
Kamanyola hosts more than 2 000 refugees and asylum-seekers from Burundi, most of who arrived in 2015 at the height of the crises in their country when President Pierre Nkurunziza clung to power at the expiry of his tenure.
Residents said the killings occurred after some Burundian refugees went to the bureau of intelligence in Kamanyola to inquire about four detained refugees.
The death of a soldier during the protests is said to have triggered the bloodbath.
"UNHCR also calls for an investigation into this tragic incident", UNHCR local spokesman, Andreas Kirchhof, said.