The approval of a trial of medicinal cannabis that had been granted by Norfolk Island's government has been overturned by the Commonwealth.

The island's administrator, former Liberal MP Gary Hardgrave, vetoed the decision made by Norfolk Island's authorities.

Earlier this month Norfolk Island gave Tasman Health Cannabinoids (THC) approval to grow medical cannabis.

The trial was originally proposed for Tasmania but the state Liberal Government rejected the bid citing concerns over safety and security, as well as potential damage to the state's lucrative poppy industry.

THC CEO Troy Langman said he was notified of the decision about the Norfolk Island trial by email.

"The reasons were exactly the same reasons we were given in Tasmania recently suggesting that we hadn't addressed all the concerns that the government had," he said.

Mr Langman said he would now focus his attention on Tasmania once again.

"We'll never give up on Tasmania... Tasmania offers a particular climate that suits important genetics, cultivars or strains that we'd like to grow," he said.

Tasmania's shadow attorney-general Lara Giddings said the Norfolk Island decision had put more pressure on the governments of Tasmania and Australia to resolve their issues with medicinal cannabis.

"It is ridiculous that Liberal governments and now their appointees are finding reasons to stop the development of a medicinal cannabis industry rather than help a properly regulated and administered industry grow, in-line with poppies," she said.

Norfolk Island's Health Minister Robin Adams said earlier this month she thought the trial was a "great opportunity both for the economy of Norfolk Island whilst providing a much needed medical product for export".

"We have our own dangerous drugs legislation and that legislation was amended with the consent of the Commonwealth of Australia back in 1997," she said.

"As a result of that legislative change I may grant a licence to import cannabis into Norfolk Island, export from Norfolk Island, plant, cultivate tend or harvest cannabis and sell cannabis," she said.