The Prime Minister wants to stop people having to fill out departure cards when they leave the country.
Photo: RNZ / Cole Eastham-Farrelly
Australia has already put an end to the practice, and Jacinda Ardern said she would like to do the same.
She said members of the Australia-New Zealand Leadership Forum had raised the matter with her.
Ms Ardern said she would be asking Statistics Minister James Shaw and Customs Minister Meka Whaitiri to start moves on it.
She had already talked to them about removing what she called this "bugbear".
Travel Company, House of Travel is backing the move.
House of Travel's Commercial Director, Brent Thomas, said the move will help make travelling easier.
"Airport companies around the country and the world have tried to make it as easy as possible, so anything that does make it easier will be welcomed."
Mr Thomas said there have also been questions in the past about the validity of the cards and the data which is gathered from them.
"A lot of people have said if I'm going to two or three countries what do I put on it? And we're not sure if they get all the cards and use them or just take a sample."
However, he said he could see the validity for inbound cards, especially to find where customers are coming from.
Statistics New Zealand has already completed an initial review of paper-based departure cards.
They believed New Zealand would be able to remove paper-based departure cards by either late 2018 or mid-2019, depending upon resourcing.
