They have issued a warrant to arrest Dariush Talagi, Detective Senior Sergeant Craig Bolton said.
Bolton said there was no risk to the public but Talagi was "considered dangerous".
He has distinctive facial tattoos, Bolton said.
"Our message to Dariush would be to hand himself in, or for anyone who sees him to call us immediately," he said.
Bolton said anyone who sees Talagi or knew of his whereabouts should call police on 111 and quote the file number 230804/3339.
People can also give information anonymously via CrimeStoppers on 0800 555 111, Bolton said.
A man shot on Queen St died yesterday and police launched a homicide investigation.
Police earlier revealed up to four shots were fired during the overnight shooting in downtown Auckland.
One man was shot in the head and another in the abdomen during an altercation just before midnight.
Bolton said the man "was taken off life support and sadly succumbed to his injuries with family beside him".
The other shot man remained in a stable condition at Auckland City Hospital, police said yesterday.
Earlier, Bolton wouldn’t comment on whether the incident was gang-related or the exact number of people involved, but confirmed police could be looking for more than one person.
"A small group of people were witnessed fighting before one offender pulled out a firearm and fired several shots," Bolton said.
He said police believed it was an isolated incident and there was no risk to the public.
Bolton said CCTV footage is helping with lines of inquiry. The offender was on a Lime scooter before and after the incident.
"What I can say at this stage, was two groups were unknown to each other and the rest of it just forming part of our investigation."
Bolton said that during the incident there were "words exchanged" which led the person to get off the scooter and approach.
"I’m very concerned about the victims who were going about their own business, they weren’t looking for trouble."
A Lime spokesperson said the company was assisting police with inquiries.
Footage from the scene showed armed police surrounding a person on the ground. Photos of the scene also show multiple scooters lying on their sides. A witness told the Herald he heard multiple gunshots and people yelling before looking out of the window to see a man lying on the ground and another being tended to by police.
Police closed off a section of Queen St after the shooting, before reopening it at 7am.
