A referendum on the issue was promised as part of a deal by Jacinda Ardern's Labour Party to get support from the Green Party to form a government after last year's general election.
Justice Minister Andrew Little now says lawmakers are tossing up between holding it next year or at the same time as New Zealand's government elections in 2020.
"It would be convenient to have it then [in 2020 since] we've got a general election so we're already running a ballot there," he told Radio NZ.
"On the other hand, there would be other colleagues who would say: 'Well we don't necessarily want a general election run on this particular sort of issue'."
But with even the question for the referendum still to be decided, the vote was unlikely to happen before late 2019 either way, he said.
Nearly 39 percent per of Kiwis who took part in the 2017 Global Drug Survey said they had used cannabis in the past year.
A bill that would create a legal defence for terminally ill people with less than a year to live to posses and use cannabis products for medicinal purposes is currently being considered by a parliamentary committee.
