He also stressed that defence and security forces could resort to force "only as a last resort" and in accordance with worldwide norms, and urged "the authorities to promptly open criminal investigations".
More than 100 refugees were accused of overrunning a jail to demand the release of four Burundians who were arrested on Wednesday night and due to be expelled from the country.
No-one with refugee status "is supposed to have an assault rifle", he said.
Eighteen Burundian refugees were killed Friday, said Mwanamboka and the others died Saturday, according to reports.
Out of 40,000 Burundian asylum-seekers, 28,000 who fled hostilities in their country were identified by the DRC's National Commission for Refugees in Kamanyola.
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The agency said it had sent teams to Kamanyola, including medical staff to see to those injured.
Soldiers and police opened fire as the refugees tried to free some of their compatriots in Kamanyola, a town in the eastern Democratic Republic of Congo near the Burundi border.
"We do not yet understand how the people who are being called refugees were also shooting at Congolese soldiers", Mende said.
Many fled political violence at home in 2015, when President Pierre Nkurunziza successfully pursued a disputed third term amid deadly protests.
Burundi's government firmly rejected the allegations, accusing the United Nations investigators of being "mercenaries" in a Western plot to "enslave African states".