But in a report on the bill, the ACT government said it could not rule out people being prosecuted under Commonwealth laws.
"It is important to note that, even after the passage of this bill, possessing and growing cannabis will carry a degree of risk arising from interactions between Territory and Commonwealth law," it said.
Mr Pettersson said a defence exists for cannabis use under Commonwealth law if the use is excused or justified by state or territory law "Commonwealth law has been written with the express understanding that there are differences," Mr Pettersson said.
"I don't think it's particularly likely the Commonwealth government will try to fight this." Federal Attorney-General Christian Porter said the bill was a matter for the ACT, but where Commonwealth laws applied they remained enforceable.
A spokeswoman for ACT Chief Minister Andrew Barr said the government had consulted with ACT Policing and the Commonwealth Department of Public Prosecutions.
A spokesman for federal Health Minister Greg Hunt said any problems with Commonwealth law were a matter for the Attorney-General, but the federal government did not support legalising cannabis for recreational use.
Amendments made to the original bill require cannabis to be kept out of reach of children, and barring adults from using it near children or growing it in community gardens.
Mr Pettersson said his motivation for introducing the bill was to make drug use a health issue not a criminal one.
"Because of our drug laws, getting caught with a small amount of cannabis can ruin your life," he said.
Earlier he said it would be a waste of the federal government's time to strike down the law.
But it wouldn't be the first time laws introduced by the territory have clashed with federal laws.
In 2013, the capital legalised same-sex marriage only to have the federal government revoke the law after it took a challenge to the High Court. Before that, in 1995, the Northern Territory legalised voluntary euthanasia only to have the federal government later legislate to stop the nation's territories from specifically introducing assisted dying.