"Marijuana is a gateway drug. The risk of graduating to ice or to heroin from extended marijuana use is real and documented," the minister told reporters in Melbourne.
"We do not believe it is safe, responsible or something which should be allowed."
Asked why the government wouldn't want the tax revenue, Mr Hunt said it didn't want to put the mental health of Australians at risk.
But Senator Di Natale argues governments around the world are realising that prohibition of cannabis causes more harm than it prevents.
"It's time Australia joined them and legalised cannabis for adult use," he said.
The minor party wants to redefine cannabis as a legal substance, with licences issued for its production and sale.
A national agency would be established to issue licences, monitor and enforce conditions and oversee regulations.
It would also act as the single wholesaler for cannabis - purchasing cannabis from producers and selling it in plain packaging to retail stores.
Up to six plants could be grown for personal use and strict penalties would be imposed on selling cannabis to minors or without a licence.
Senator Di Natale said almost seven million Australians had tried or used cannabis, with consumption and drug possession-related arrests both on the rise.
The Greens leader, a former drug and alcohol doctor, pointed to a recent poll showing 55 per cent of Australians believed cannabis should be regulated and taxed like alcohol or tobacco.
He expects the plan to raise hundreds of millions of dollars in revenue, helping fund treatment, education and other harm reduction programs.
Alex Wodak, president of the Australian Drug Law Reform Foundation, welcomed the announcement.
"Banning cannabis hasn't reduced its use or availability, yet it has distracted police from following up more serious crimes, harmed a lot of young people and helped make some criminals rich," Dr Wodak said.