International flights from Auckland Airport have been delayed and four flights from Australia cancelled.
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An airport spokesperson said Immigration New Zealand's passport processing software was experiencing outages, delaying flight check-ins.
Immigration New Zealand (INZ) has confirmed its overseas check-in system - operated by Swiss technology company SITA - used at airports is down.
"INZ is monitoring SITA's progress in getting the system up and running as soon as possible. We are also working with airlines to minimise any disruption to travellers," a spokesperson said.
"Check-in agents are now relying on manual checks with INZ staff to verify information."
Passengers could still manually check-in but should contact their airlines for the latest information, the spokesperson said.
A spokesperson for Wellington Airport said it was a global network problem affecting all airlines, and did not say whether flights had been affected.
In Australia, Jetstar said it was working to bring systems back online after flight delays and cancellations, including four New Zealand flights that were cancelled due to the issue.