One passenger said his flight's international departure was delayed for an hour.
Air New Zealand said flight NZ729 to Melbourne was delayed by 20 minutes "as a result of an issue with security screening".
"Customers are advised to check the arrivals and departures page of our website for the latest security information."
The airport has not yet confirmed how many passengers were delayed.
The airport earlier declined to comment on the cause of the security issue. A spokesman said: "Some travellers at the international terminal are experiencing longer-than-usual queues at aviation security and a number of flights have been delayed.
"This followed a security incident, which has now been resolved. Security is always our highest priority and we ask for travellers' patience."
An additional statement at 7.35pm said queues had returned to normal levels and the airport thanked passengers for their patience.
Comment has also been sought from police.
On Friday the airport briefly diverted or held flights after debris closed a runway.
A patch-up of the surface took about 20 minutes. A number of regional services were affected.
MORE TO COME