His vehicle - a Hyundai Santa Fe - was found at Piha Beach car park two days later.
Sergeant Tania Kingi said police understood how "devastating his disappearance has been for his family" and that their hearts went out to them.
"The police staff involved in this investigation wanted nothing more than to be able to provide the answers that the family so desperately seeks at this time, and it is unfortunate that we have not been able to achieve this, despite our best efforts."
Since his disappearance and the discovery of his vehicle in Piha, police have carried out multiple land searches in the surrounding area, she said.
"We have also undertaken several aerial sweeps of the region, while ground searches have also been carried out across the wider Waitakere coastal area.
"Sadly, none of these searches has uncovered any trace of Laurence."
Kingi said police had issued multiple public appeals for information and as a result had spoken to a number of people in the Piha area, and those who were last in contact with Wu.
CCTV footage was extensively reviewed, including footage of when he was last seen on Sainsbury Rd.
Police also examined the contents of his vehicle, including his laptop, as part of their investigation.
"After completing all lines of inquiry, there is no evidence to suggest foul play in connection with his disappearance.
"Police are not treating his disappearance as suspicious and the matter is being referred to the Coroner.
"We have been working closely with his family and our sympathies are with them at this difficult time."
WHERE TO GET HELP
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• LIFELINE: 0800 543 354 or 09 5222 999 within Auckland (available 24/7)
• SUICIDE CRISIS HELPLINE: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• YOUTHLINE: 0800 376 633 ,free text 234 or email talk@youthline.co.nz or online chat.
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757
• SAMARITANS – 0800 726 666.