Air New Zealand's first direct flight from New York touched down at Auckland Airport.
The 17-hour flight from the John F Kennedy International airport touched down about 8.30am but many passengers were without their luggage.
One said only business class and Koru members had their bags.
Another told RNZ that more than half the plane's luggage was still in New York.
Air New Zealand chief operating officer Alex Marren apologised for the luggage being left behind.
"Unfortunately given additional fuel requirements due to adverse weather, some customer bags were unable to be loaded in New York and we are getting them to New Zealand as soon as possible. We are in touch with customers to update them and reunite them with their bags. We're sorry for any inconvenience this has caused."
The flight is the longest Air New Zealand has operated, and the fourth longest flight in the world.
Travellers from New York were welcomed off the Boeing 787-9 Dreamliner aircraft on Monday morning with a kapa haka performance.
Air New Zealand general manager Auckland airports Tessa Auelua said it was a huge milestone for the company.
A year of planning had led up to this moment, she said.
Auelua expected passenger numbers from the United States would bounce back quickly with the reopening of borders.
The new route was announced in April as part of the airline's partnership with US-based United Airlines.
The first flight departed Auckland at 4pm on Saturday with a scheduled flight time of 16 hours and 15 minutes.
The return journey which arrived this morning was expected to take 17 hours and 35 minutes due to the difference in jet streams.
The new route has been given the flight numbers NZ2 for Auckland to New York and NZ1 for New York to Auckland.
When announcing the route, chief executive Greg Foran said the numbers were traditionally used for an airline's flagship route "And that's what New York will be - our flagship route," he said.
The airline will operate the route three times a week.