"A number of reports of potential sightings of Bourne have been received this week and these have been followed up by police, with inquiries made at multiple addresses across the wider Auckland region."
Police were are also now seeking Serene Tilsley, 21, who is associated with Bourne and has a warrant to arrest in relation to the incident.
"Police are also appealing for sightings of a black 2005 Ford Falcon saloon – registration CTS862 – linked to this incident, which was seen in Pakuranga on Sunday morning."
Bourne is considered dangerous and should not be approached by the public.
"The investigation team will continue to do everything possible to locate Bourne so he can be held to account.
"We are appealing to Bourne to hand himself him so this can be resolved without further incident," says Detective Inspector Beard.
Police acknowledged members of the public who had contacted them with information about possible sightings of Bourne.
Anyone with information about the whereabouts of Desmond Bourne and Serene Tilsley or the Ford Falcon vehicle was urged to contact Waitemata Crime Squad on 09 839 0697, or Crimestoppers anonymously on 0800 555 111.
Support was being provided to the family of Zane Smith, Beard said.