The call sets up the possibility of a diplomatic confrontation between the United Nations and the government of President Joseph Kabila.
The government had said it would accept UN technical assistance but wanted to retain control of the inquiry in response to a Thursday deadline by UN High Commissioner for Human Rights Zeid Ra'ad al-Hussein for Congo to agree to a joint probe.
But in his statement on Friday, Zeid said the government "response to date falls short" and urged the UN Human Rights Council, which is holding a session until June 23, to act.
Government spokesman Lambert Mende told Reuters the government was not willing to go beyond its previous offer to run the investigation itself and accept UN technical help.
Hundreds have been killed and 1.3 million displaced in central Congo since last August in fighting between a militia and government forces. Violence has risen nationally since Kabila decided to stay in power beyond the December 2016 end of his mandate.
"The international community is throwing its weight behind ensuring that the endemic impunity in the DRC is brought to an end," Zeid said.