A BBC reporter saw 21 in one district of Bujumbura and local officials spoke of 13 in another. Most appear to be young men killed by gunfire, some with their hands tied behind their backs.
The bodies were found a day after attacks on three military sites.
Unrest has blighted Burundi since an attempted coup in May and protests over the president’s continued rule.
The coup attempt followed President Pierre Nkurunziza’s decision in April to seek a third term in office.
He won a third term in a disputed election in July.
The largest number of bodies found on Saturday were in Bujumbura’s Nyakabiga district, a focus of anti-government protests.
Others were discovered in the southern neighbourhood of Musaga. There are reports of more bodies in other parts of the city.
Residents accuse the police of detaining young men during house-to-house searches on Friday and then executing them.
But a police spokesman told Reuters there were no “collateral victims” and that those killed had been behind attacks on government installations.