A row is brewing between the ACT and Federal Government over controversial moves to legalise cannabis in Canberra from early next year.

Federal Health Minister Greg Hunt has penned a letter to ACT Chief Minister Andrew Barr, calling on him to produce any evidence he considered before supporting the legislation, regarding the health impacts of cannabis.

The ACT Government last month passed legislation legalising possessing, smoking and growing small amounts of cannabis from early next year.

Adults can possess up to 50 grams of dry cannabis and grow two plants.

The passage of the laws appeared to take many within the Federal Government by surprise, and prompted a strong response, with some senior Government ministers labelling it "crazy" and suggesting the ACT Government was spending "too much time smoking hooch".

Mr Hunt wrote to Mr Barr this week detailing his concerns around the potential health impacts of the legislation, and querying how his Government came to support the private members bill.

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"I have serious concerns the ACT's legislation will result in further health harms and exacerbate mental health issues, particularly for those who have a family history of mental health disorders," he wrote.

"I note that both the Australian Medical Association and the Royal Australian College of Surgeons have also expressed concerns over the legislation, with the latter calling for it to be reversed."

Mr Hunt attached a dossier of research and briefings on both the physical and mental health effects of recreational use of cannabis, to back up his claims.

"I call on you to explain whether the ACT Government considered the international evidence on the health effects of cannabis and to provide any evidence to the contrary," he wrote.

Within the letter, Mr Hunt noted the global direction on regulation of cannabis was towards legalisation and decriminalisation, but he suggested that was prompting more research into its adverse effects.

A spokeswoman for the ACT Government said they intended "to respond fulsomely to Mr Hunt's letter" in the coming days.

The health impacts of the legislation are not the only potential point of conflict between the Federal and ACT Governments over the contentious legislation.

Federal Attorney-General Christian Porter is still considering the legalities of the bill, although the final version of the legislation is yet to be published.

The ACT laws directly conflict with Commonwealth legislation, which prohibits the possession of cannabis.

Mr Porter has not ruled out seeking to have the laws overturned.