"I have no problem with the medical use of marijuana, just as I have no problem with the medical use of opiates," Abbott wrote to talkback radio host Alan Jones in a letter dated Aug 23, Sydney Morning Herald reported.
Jones read out the letter from Abbott -- who has not commented publicly on the issue before -- on his 2GB breakfast programme Wednesday.
Jones has been campaigning on behalf of Dan Haslam, a cancer patient, who has been using marijuana to relieve nausea associated with chemotherapy to treat his terminal cancer.
The peime minister's intervention was welcomed by Haslam's mother, Lucy, who has launched a popular online petition to decriminalise marijuana for pain relief.
Earlier, The Uniting Church had also urged the Western Australian government to consider legalising marijuana for medicinal use.
The New South Wales government announced Tuesday that a clinical trial into medical marijuana will report back to the government by the end of the year.
In the US, Colorado and Washington have legalised the sale of marijuana for medical and recreational use.
A spokeswoman for Abbott confirmed the letter reflected Abbott's views on the issue.