In February, Dunne said in a blog post that a register for terminally people who were using cannabis was "worth further consideration" if it offered vulnerable people "a little more assurance at a very stressful time of their lives".
In New South Wales, dying patients can voluntarily add their names to a register to ensure they and their family are not harassed by police.
"I've talked to New South Wales people about it," Dunne said.
"It's fraught with considerable difficulty, and ... they're concerned that what they are doing is giving sanction to illegal activity."
Dunne said the policy in New Zealand was that people who were using cannabis for medicinal purposes were not pursued by police.
"It strikes me, on balance, that our more pragmatic solution is arguably better than having a formal, rigid position like the NSW register."
However, Nelson lawyer and campaigner Sue Grey told Parliament's Health Committee today that medical cannabis use was still being criminalised in New Zealand.
"I get called by people every week. A triple amputee with phantom pains was prosecuted by police last week for using medical cannabis in his own garden on the West Coast.
"A young mother who's had a series of chronic back issues, she's been in and out of the emergency ward of hospital. The police raided her medical cannabis that was the one thing that was giving her a cure and letting her keep going.
"Not only are the very illest people in New Zealand currently being punished, but their medicine is being taken away."
Dunne said he could not comment on individual cases, and noted that other factors may have led police to intervene.
"I think that people who are in a terminal or serious situation and who are using marijuana for pain relief - I don't that that should be a priority for the police.
"I would be concerned if it were to become one. At a general level, my assurances have been that the police have a similar view to me."
It was not known whether police were only turning a blind eye to terminally ill cannabis users, or whether the informal approach was applied more broadly.
Grey appeared alongside Rose Renton, who has submitted a 17,000-signature petition calling for easier, cheaper access to medical marijuana in New Zealand.
Renton's son Alex was the first person to get approval to use medical cannabis in New Zealand before his death in July 2015. She told MPs she was contacted every day by people who were "desperate, dying and terrified of our laws and what to do next".
