A Burundian refugee said that more than 30 had been killed and at least 100 wounded in the violence yesterday.
Interior ministry official Josue Boji said troops had tried to disperse the refugees by "firing in the air but were overwhelmed" when the group responded by throwing stones.
Boji said the clashes began after a group of refugees overran a jail run by the country's domestic intelligence agency to demand the release of four Burundians who had been arrested for expulsion on Wednesday night.
Boji had warned earlier that the toll could rise further, as the refugees took the bodies of other victims to the Pakistani-run UN camp at Kamanyola.
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A spokeswoman for MONUSCO, the UN's peacekeeping mission in the country, gave a toll, which was also provisional, of 18 dead and 50 injured.
A Burundian refugee told AFP: "I saw people falling down, men, women and children who were completely unarmed.
"So far, we have counted 31 dead and at least 105 injured, 15 of them seriously," the refugee said.
Tens of thousands of Burundians have fled to the eastern DR Congo to escape a wave of violence that unfurled in 2015 after Burundian President Pierre Nkurunziza sought a fiercely contested third term in office.
Overall, the violence in Burundi has claimed between 500 and 2,000 lives, according to differing tolls provided by the UN or NGOs and more than 400,000 Burundians have fled abroad.
Around 36,000 are in DR Congo, mainly in the overcrowded camp of Lusenda, in the east, or several transit camps.
They fear religious persecution if they are sent back home, they said.
On September 4, the UN released a report accusing Burundi's government of crimes against humanity, including executions and torture, and urged the International Criminal Court (ICC) to open a case "as soon as possible".
Burundi's government firmly rejected the allegations, accusing the UN investigators of being "mercenaries" in a Western plot to "enslave African states".