Airways New Zealand, which provides navigational services, wrote on Twitter that it experienced a radar failure at about 2:48 p.m. (0248 GMT).
It said in a later statement that it had identified the issue, tested the system, and resumed full service about two hours after the flights stopped. The agency did not say what caused the problem. It said that "at no point was the safety of any airport operations compromised."
The agency said its priority was resolving the issue and staff would not be immediately available for interviews.
Transport Minister Simon Bridges said that after the failure, aircraft that were aloft were able to land in a staggered fashion, with air traffic control able to communicate with the planes via radio contact.
National carrier Air New Zealand said about 160 of its international and domestic flights had been affected. It said it had resumed flights Tuesday afternoon but the backlog would take some time to clear.
Spokeswoman Marie Hosking said that international flights were being given priority, followed by larger domestic jet flights and finally smaller domestic flights.