Operation Likofi (which means "punch" in the local Lingala language) claimed at least 42 victims, including four children, many of whom were shot in their own neighbourhoods or even walking out of their homes, the UN's human rights office in Kinshasa said.
The report said at least nine people had been summarily executed and 32 were forcefully "disappeared," but warned the number could be far higher as many witnesses and relatives of victims refused to speak out for fear of retaliation.
The UN said a high-ranking officer in Kinshasa had overseen the killings and several other police had carried out the orders, which happened during a police crackdown on Kinshasa's gangs.
Known as "kuluna", the youths roam the streets in packs armed with machetes, often under the influence of drugs or alcohol, snatching bags, jewellery and mobile phones and sometimes killing those who dare to resist.
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The gangs had terrorised the streets of Kinshasa, a city of some 10 million, before the start of operation Likofi, which ran between November 2013 and February this year.
"I am appalled by the gravity of the human rights violations documented in this report and I call on the Congolese authorities to bring to justice without delay the perpetrators," human rights commissioner Zeid Ra'ad Al Hussein said in a statement.
The UN urged Congolese authorities to lead "prompt independent, credible and impartial investigations" into the police killings and to "prosecute all alleged perpetrators of these violations, regardless of rank".
The UN report also published a letter of response from the Congolese Interior Minister Richard Muyej, which said legal proceedings had been taken against several police officers involved in the operation, without saying how many.