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Air New Zealand Chief Operational Integrity and Safety Officer David Morgan confirmed the pair were removed from Flight NZ424 as they were not following crew instructions.
The incident resulted in a delay of 25 minutes, he said, and apologised for the inconvenience to passengers.
A police spokesperson said they were notified that two people were asked to disembark for not following airline crew instructions, and officers accompanied the pair back to the check-in desk.
A passenger on the flight said they saw an elderly woman being led from the plane with teary eyes.
The flight captain told passengers the airline would take steps to follow through on the incident.
“They may find themselves not flying with us for a wee while,” he said.
The Air New Zealand Code of Carriage lists several potential reasons for refusing carriage or service to a passenger, including the passenger refusing to obey instructions, causing offence or discomfort to others, or causing or involving risk to themselves or others.