But Mr Gunner has gone further, setting up a parliamentary committee to look at "harm reduction" strategies in relation to illicit substances, including the possible decriminalisation of marijuana and other drugs.
Decriminalisation means removing penalties such as jailing or conviction with a criminal record, although it does not make a product legal and there is no suggestion it would be legalised in the NT yet.
"We are going through a parliamentary committee process to look at essentially addictive behaviours and policies around that, which could include decriminalisation," Mr Gunner told reporters.
"I do think it is going to be become a more common topic in Australia, we have not always been as progressive as other parts of the world but I don't think it's beyond the realm of discussion anymore.
"We recognise we have got to do policy work, there seems to have been some good outcomes in having a health-based approach in other parts of the world that I am interested in."
He cited the examples of American states, including nine where marijuana is fully legal for recreational use and 13 where it is decriminalised and Portugal where all drugs have been decriminalised.
However he said that did not mean it would work well if applied to the NT, where cannabis is a major problem among Aboriginal people, and that was why policy work was needed.
Australian Medical Association NT president Robert Parker has written to Greens Leader Richard Di Natale, asking him to change his policy supporting legalisation and pointing out the indigenous problem with illicit substances and psychosis.
The federal government could veto such a move - as occurred when the NT legalised euthanasia in 1996 - but a spokesman for federal Health Minister Greg Hunt said decriminalisation was a matter for the NT government and police.
A trial cannabis crop has already been grown around Katherine, south of Darwin, with the climate found suitable.
Mayor Fay Miller is excited about the prospect of a medicinal cannabis and hemp industry, saying she has friends that have enjoyed significant pain relief using marijuana.
"I am very happy for any development that provides great economic growth, it is super, super, super," she told ABC radio.