Zion Purukamu, 16, died in hospital after being stabbed at a house party in Medbury Tce in the upmarket Christchurch suburb Fendalton on Friday night.
A 17 and 14 year old were also stabbed, and remain in hospital in a serious but stable condition.
Police have not yet arrested or charged anyone.
Detective Inspector Michael Ford said interviews with people who were in the area at the time were continuing.
However, he said there were more people at the party who had not yet spoken to police.
He urged everyone who attended to make contact - even if they thought they had nothing of relevance to say.
The company that manages the rental house where the party was held said they would have shut down the party if they knew it was happening.
Christchurch Holiday Homes director Sue Harrison said the news of the death was devastating.
"We do all we can to prevent this, this is the worst thing, so all of our policies are around no parties and no extra guests even visiting the property after 10pm," she said.
"These are the conditions the booker signed up to so they've conned us."
The conditions included no parties, Harrison said.
"We've been doing this for many years, since prior to the earthquakes, and we've never seen the likes of this. And it's something you hope you never, ever see again."
Harrison said external cameras would be installed at some properties, to monitor who is coming and going.
Ilam MP Sarah Pallett said on Sunday the community was reeling after the stabbings, which had hit close to home.
"It's an absolutely devastating piece of news ... I'm a mum with daughters between 12 and 26, so I can only imagine what the families must be going through."
Police are still appealing to the public for any CCTV or other video of the incident.
