Tuuholoaki was gunned down on August 3 on Auckland’s Queen St in the city centre in what’s been described as a drive-by-style shooting.
A second man was also shot and injured.
Witnesses described seeing the shooter then flee on a scooter.
Tuuholoaki is understood to have moved to New Zealand from Australia last year.
Police said the manhunt for 24-year-old Talagi is continuing.
“The investigation team remains committed to locating Talagi,” Detective Senior Sergeant Craig Bolton of Auckland City CIB said.
“Anyone found to be aiding or assisting Talagi to evade police in any way may be liable to prosecution for being an accessory after the fact.”
Bolton warned that Talagi is considered dangerous and should not be approached.
“If you sight him, please call 111,” he said.
Anyone with additional information on the whereabouts of Talagi should call police on 105 or go online to https://www.police.govt.nz/use-105, police said.
Those with information can cite the reference file number 230804/3399.
Information can also be provided anonymously through Crime Stoppers on 0800 555 111.