Mr Rattenbury this week wrote to environment commissioner Professor Kate Auty, ordering a full review of the scheme, including a "triple bottom line" assessment and cost-benefit analysis of the ban to see how it could be improved.

While the ban is enforced by Labor, through regulatory services minister Gordon Ramsay's portfolio, the Greens minister, who has previously called for it to be tightened, holds responsibility for the ban itself.

The 2012 ban forced retailers to take light, single-use plastic bags off the market in the ACT, but allowed them to keep selling heavier, often branded, plastic bags as long as they were thicker than 35 microns, as well as fully biodegradable bags.

Mr Rattenbury said while the ban had led to 'positive behaviour change", he wanted to ensure it was working as well as possible and improving environmental outcomes.

"I'm worried about the extent to which retailers are using slightly thicker plastic bags, which is currently permitted," he said.

"Plastic is an environmentally damaging waste that is produced from fossil fuels, does not break down quickly, and is hazardous for our wildlife and oceans.

"We may be able to refine the scheme to ensure we further reduce the use of plastics, for example by only permitting single-use bags that are biodegradeable."

A review of the scheme in 2014, which examined the total tonnage of plastic bags going to landfill in two six month periods found it cut plastic bag waste from 266 tonnes before the ban to 171 tonnes afterwards, or a reduction of about 36 per cent.

A survey of about 600 Canberrans completed for the review found while 65 per cent of respondents supported the ban, some 34 per cent said they either did not support it because it was ineffective or because they objected to having to buy bin liners to replace the plastic bags they previously used for that purpose.

In his letter to Prof Auty, Mr Rattenbury wrote that "plastic bag manufacturers were quick to ensure that they were able to offer bags that were just over the 35 micron minimum limit to retailers".

"As a consequence I understand that many retailers and customers have not changed their behaviour around the use of plastic bags, and perversely may instead be using thicker plastic bags for single uses," the letter reads.

Mr Rattenbury wrote that he had considered several options to extend the ban, including increasing the legislated thickness of bags sold by retailers, or changing the scheme so only fully biodegradable bags could be offered to customers.

The review, he wrote, would also need to make recommendations as to "how and whether improvements could be made to improve overall environmental outcomes".

Prof Auty is expected to report back her findings and recommendations by June this year.