One person has been arrested after the death of 16-year-old Zion Purukamu at a party in a rented Airbnb home in Christchurch on Friday night.

A youth has been charged with murder and two counts of wounding and is due to appear in the Christchurch Youth Court on Tuesday.

Police said Zion's family had been advised of the arrest and they thanked the members of the public who had provided information so far.

"Operation Medbury remains an active investigation and police still want to speak to people who were at the party when the incident occurred," a police spokesperson said.

"Anyone with information that could assist our investigation or anyone who is yet to come forward is asked to contact police on 105 and reference Operation Medbury."

Zion died after being injured at a party in Fendalton on Saturday night.

Two other victims were also stabbed - one aged just 14 and the other 17 - and are in a serious condition in Christchurch Hospital.

Police have said about 80 young people were at the party.

It was held at a house rented through Airbnb on Medbury Terrace, described as "a quiet cul-de-sac".

Earlier on Monday, Zion's family released a statement.

"Zion's family would like to thank the wider Christchurch community for the support and aroha they have been shown over the past few days," they said in the statement provided by police.

"At this time, they are requesting privacy to focus their efforts on the funeral preparations.

"They would like to thank those who have come forward to share information with police and encourage anyone who is yet to come forward, to please do so."