Two days of violence saw at least 140 people injured, 299 arrested and 53 people killed, the UN report said.
The dead included four police officers, and protesters were responsible for killing at least three of them, the report said.
The government did not immediately comment on the report.
Opposition parties had called for the September 19 demonstrations to protest the election delay, calling it an effort by Kabila to hold onto power.
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The UN Special Representative of the Secretary-General for Congo, Maman Sidikou, urged Congolese authorities to conduct independent, credible investigations and bring perpetrators to justice.
"This is particularly crucial in this volatile pre-electoral context," Sidikou said.
A 5-year-old child was among the vast majority of victims who were shot by security forces, including the national police, republican guard soldiers and army, the new report said.
Local and international journalists were harassed, detained and arbitrarily arrested.
Many people worry such violence will worsen as elections, once scheduled for November 27, are now expected in early 2018.
The agreement came a day after Congo's constitutional court approved a request by the electoral commission to postpone the vote.