The Labour Party leader is set to govern New Zealand with a coalition government, made up of her own party, the Green Party of New Zealand and the populist party, NZ First.

"During the campaign I've always been very vocal about the fact that I do not believe people should be imprisoned for the personal use of cannabis. On the flip-side, I also have concerns around young people accessing a product which can clearly do harm and damage to them," she said.

Jacinda Ardern told reporters Friday that she will work with her Cabinet and take advice before deciding on any referendum date.

The newly-elected prime minister of New Zealand has said she wants a national discussion on legalizing cannabis.

A proposed change in the law over cannabis is being driven by the Green Party manifesto which states the drug should be legal for personal use, including possession and cultivation.

The Greens also want to introduce a legal age limit for personal use and remove penalties for anyone growing for medical use.

The Executive Director at New Zealand Drug Foundation, Ross Bell, said he regularly sees 65 percent in favor of changing the law in the polls his organization conducts, and believes a fresh look at drug policy is overdue.

"It is over 40-years-old and like many other countries, successive governments have not wanted to engage on this issue," Bell told CNBC by telephone Friday.

"Lo and behold the Green Party come along, and allows the country to have the sort of conversation we should have had for a long time."

Bell cautioned that people do need to acknowledge the harm that cannabis can do in society and added that he would not want to see the pendulum swing all the way from prohibition to a free-market arena.

In Canada the government has promised to make cannabis legal by July 1, 2018 but is struggling to satisfy international legal obligations. Bell cited the current Canadian model of cannabis policy as one that New Zealand could pursue.

Timing of a referendum remains unclear but Bell said that the New Zealand government would want any vote to be binding and, if possible, held before 2020.