Mr Barr will go to the federal and NSW governments "to seek views ... on the form of an inquiry into the legacy of Mr Fluffy and to seek support for the cost of an inquiry".

His hand was forced this week by Liberal leader Jeremy Hanson, who put a motion in the Assembly calling for a royal commission-style board of inquiry into the Mr Fluffy affair, saying an inquiry should report before the 2016 election. The Greens' Shane Rattenbury, who holds the casting vote, helped Labor defeat the call, in return for Mr Barr agreeing to push the issue nationally.

Mr Rattenbury said an inquiry would ensure authorities learnt from the mistakes and prevented them being repeated. It would also allow victims to have their stories told and put on the public record, pinpoint any blame, and deal with negligence and compensation. But it would cost tens of millions of dollars and must be done properly, with the Commonwealth fully involved.

Mr Barr told the Assembly there was no point in the ACT setting up its own inquiry, given the fact Mr Fluffy loose-fill asbestos was pumped into ceilings before self-government, and the clean-up of the late 1980s and early 1990s was also managed by the Commonwealth.

If the ACT pushed ahead without the full co-operation of the Commonwealth and NSW, it risked "an undertaking that is doomed from the start" and could be derailed by arguments over jurisdiction, Mr Barr said, describing Mr Hanson's call as premature, glossing over the complexities and setting an arbitrary and unrealistic deadline for political purposes.

The Mr Fluffy story must be reviewed in a "robust" and comprehensive process that provided answers, but it should be done at the right time, Mr Barr said. An inquiry now would divert resources from the demolition scheme.

"The government is resolute in its view that the critical work of the taskforce ... cannot be distracted by the need to support or respond to an inquiry," he said. "Without downplaying the significance of the story that needs to be told, I believe the best thing that can happen for affected families and for the wider Canberra community is that we get on now with the demolition and rebuilding."

He also rejected Mr Hanson's suggestion that he was less sympathetic to the plight of Mr Fluffy families than former chief minister Katy Gallagher, saying he was close to the stories of grief, anger, loss and frustration of many families who had been part of a "merry-go-round", and he had also heard stories of great resilience and hope as families moved into new homes to rebuild their lives.

Owners of 950 Mr Fluffy homes have accepted the government's buyback offer to date, with 16 homes demolished so far.