Prime Minister Tony Abbott has thrown his support behind the legalisation of cannabis for medical purposes.

In a letter to talkback radio host Alan Jones, Mr Abbott went even further than NSW Premier Mike Baird – who has approved a clinical trial of the use of medical cannabis – by saying that no further testing should be needed on the drug if it is legal in similar jurisdictions.

Tony Abbott says he has "no problem" with the medical use of cannabis. Credit:AFR

"I have no problem with the medical use of cannabis, just as I have no problem with the medical use of opiates," Mr Abbott wrote in a letter to Jones dated August 23.

"I was under the impression that the personal use of cannabis was no longer an offence in NSW.