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The airline came under fire from Māori intellectual property rights experts earlier this month for filing the application.
Chief executive Christopher Luxon said after speaking with iwi leaders the airline will no longer actively pursue the trademark, and will urge the government to review the rules for trademarking words from the Māori language.
"The current trademark situation does not reflect the sometimes differing and legitimate views of both the Māori and legal communities."
Te Rūnanga o Ngāi Tahu chief executive Arihia Bennett commended Air New Zealand for seeking the views of Māori leaders.
She said the iwi was also urging the government to better protect Māori intellectual property.
The Māori Council executive director Matthew Tukaki said he was pleased Air New Zealand had finally come to its senses.
"I think it's great news, we started the campaign less than a week ago.
"The shame of it is, let's just admit it Air New Zealand, you were concerned about the hit to the hip pocket after CNN and the BBC and a range of international news agencies picked it up.
"My message is, why did you do it in the first place? You should have listened to everyday Māori instead of these iwi leaders that you keep on talking about that nobody knows who they are. More importantly, we as a country were celebrating Māori Language Week.
"It was a despicable act for all of this to emerge during that week."