The easing of the rules does not apply to unprocessed plant material such as cannabis oil or dried leaf.
Sushila Butt of Kaitaia, whose disabled daughter, Alisha, uses Sativex to control severe epilepsy, welcomed the change but said it did nothing to solve the problem of affordability.
Mrs Butt fought a long campaign to get access to Sativex after Alisha suffered a series of life-threatening seizures and all other treatments failed.
Alisha, 21, was granted permission to use the drug but the next problem was paying for it.
Both Mrs Butt and her husband, Royd, are full-time caregivers and Sativex, which is not government-funded, costs more than $1000 a month.
Last February the Northland District Health Board stepped in and funded the drug for Alisha, making her New Zealand's first recipient of a publicly-funded medical cannabis product.
Mrs Butt said many other families would benefit from the medication but could not afford it. Alisha still suffered from epilepsy but had not been admitted to hospital since taking Sativex. In the past she had been admitted as often as once a week, she said.
The Otamatea Grey Power has repeatedly called for the outright legalisation of medicinal marijuana, saying members wanted to have the choice of dying without pain.
President Beverley Aldridge said the government's announcement last week would not make any difference because medical cannabis would still be unaffordable.
"The middle- and lower-income earners, including retirees with deteriorating health, would not be able to pay up to $1600 a month. The changes are really for the upper class,'' Ms Aldridge said.
"What the government can do is to go back to Pharmac and say how about every person will pay $20 in prescription charge."
The Green Party welcomed Mr Dunne's announcement, calling it a small but positive step to speed up the "slow and frustrating" process of getting medical cannabis for the sick or dying.
However, Greens' health spokeswoman Julie Anne Genter said it did not address the cost issue. New Zealanders should be able to access medical cannabis, with a doctor's support, as cheaply and easily as other prescription drugs.
Recent years had seen a shift in attitudes to medical cannabis and it was time to make it completely legal, which wasn't even close to what Mr Dunne had announced, Ms Genter said.
Northland-based Green MP David Clendon said it never made sense for a politician to decide whether a patient should have access to medical cannabis. The decision should always have been a clinical one.
It seemed the government had a blind spot that demanded tight control of anything cannabis-related when many opiates, for example, were available as prescription medicines, Mr Clendon said.
With regard to funding for Sativex, Pharmac operations director Sarah Fitt said the agency took a consistent, evidence-based approach to considering funding for any medicine.
No application so far for funding Sativex had been able to show it was the best use of public money.
She expected Pharmac would continue to receive applications for funding pharmaceutical-grade cannabis-related products and was open-minded to the outcome of the evaluations.
