Zeid Ra'ad Al Hussein said the list should include summary executions, killings of children, recruitment of child soldiers and sexual violence.
Hundreds of people have been killed, many of them mutilated, and 1.3 million displaced, according to the UN, since government forces killed Kamwina Nsapu, a tribal chief and militia leader in August last year.
Victims include militia fighters, civilians, members of the security forces and two UN experts investigating mass graves. American Michael Sharp and Swedish-Chilean Zaida Catalan, were kidnapped on 12 March.
Their bodies were found 16 days later - Catalan had been decapitated and her head was never found.
So who was Kamwina Nsapu?
His name was Jean-Prince Mpandi. He was the sixth Kamwina Nsapu, the traditional chief of the Bajila Kasanga, in Kasai-Central Province.
Few details are known about his life.
He was at agricultural college in Katanga's city of Lubumbashi but dropped out before completing his studies;
In 2004-2005 he opened a traditional medicine clinic in Tshikapa, in Kasai. He claimed he had studied with Chinese doctors and had even been to China. However, he also said he was a veterinary surgeon.
He has ties with South Africa, where his family lives.
It was only recently that Mpandi attracted the attention of the authorities.
In January this year newly appointed Vice-Interior Minister Emmanuel Ramazani Shadari told parliament the government had found a 2016 document signed by Kamwina Nsapu calling on the province's youths to kick out all foreigners, except for diplomats, from so-called Greater Kasai.
Sources told RFI that he increased his influence through ritual ceremonies.
It was Ntenda, one of his cousins, who reportedly accused Kamwina Nsapu of preparing to launch an insurrection. The security forces raided his home while he was in South Africa. On his return he had barricades set up around his home - but had them dismantled after talks with the authorities.
However, in July 2016 a mob attacked Ntenda, killed at least six people and burnt down some 100 homes. Mpandi denied his supporters were involved.
The crisis accelerated when the Kamwina Nsapu and his militia stormed the town of Tshimbulu. Five police officers were among the nine people killed. Most offical buildings were razed to the ground during the attack.
On 11 August he was given an ultimatum to surrender. The next day, government security forces shot him dead.
But violence has increased since his death, with both sides accused of murder, mutilation, rape, and destruction of property.
To view RFI's webdoc in French, the first of three on the Kasai crisis, click here