The news came as a body blow to some owners of the asbestos-contaminated houses who have been holding out for an inquiry to get to the bottom of how the dangerous loose-fill asbestos insulation was allowed to be pumped into ceilings and its handling since.

Owners want to know why "Mr Fluffy" Dirk Jansen was allowed to sell and install the asbestos insulation for more than a decade from from 1968 until 1979, despite warnings from federal bureaucrats about the dangers.

They want scrutiny of the clean up program of the late 1980s and early 1990s, when 65,000 homes were surveyed and about 1080 homes were found to contain the asbestos. It was removed from the ceilings, but not from the walls or subfloors of houses, and it was only after the 2013 discovery of a Downer home missed in the clean up, where the extent of contamination of walls and subfloors was revealed, that the ACT government decided to buy back and demolish every Fluffy home.

Fluffy owners also want to know why owners were allowed to sell and rent Fluffy homes over the last 25 years without warning new owners and tenants. And why the ACT government approved extensive renovations, exposing owners and tradespeople to the toxic asbestos dust, without explicit warning.

But given the ACT did not get self-government until 1989, Mr Barr said a board of inquiry needed "participation and engagement" from the Commonwealth and NSW to access records and to share the significant cost. He had raised the issue with Prime Minister Malcolm Turnbull and NSW Premier Mike Baird and "neither have indicated support", Mr Barr said.

Asked to clarify, Mr Barr said he had asked for "financial support for a process that looks at the history of the issue", but it had "not been forthcoming".

He maintained his commitment to "a review of the history ... at the conclusion of the eradication program". Demolition is scheduled to continue until about 2020.

Mr Turnbull's office declined to comment.

A board of inquiry is the ACT's equivalent of a royal commission, with the power to compel witnesses and subpoena documents.

Constitutional lawyer George Williams said there were limits to the ability of states and territories to compel some federal documents, if the Commonwealth did not give them voluntarily – including ministerial documents and others with special protections.

"It is true that the territories and the states don't have extensive powers in that regard. They can't compel everything they want," Mr Williams said. "[But] if they are run-of-the-mill documents that nothing special attached to then it's not clear there is a problem."

Fluffy owner Felicity Prideaux said owners were "absolutely mortified".

"We have people who have lost their homes, their lives have been ruined, they have lost their home businesses, we have people who have health issues related to stress, relationships that have completely broken down, children who are absolutely devastated because they still want to go back home."

"The fact that the chief minister has now backed off from having a board of inquiry into this debacle cheats the Canberra community of an understanding of what happened and it certainly has just created a lot more stress in the Fluffy community. They need to know."

Mrs Prideaux is a spokesperson for the Fluffy Owners Full Disclosure group, which is highly critical of the government's buyback.

But the highest profile Fluffy owner, Brianna Heseltine, who fought hard for the buyback in 2014 and heads the Fluffy Owners and Residents Action Group, took the opposite view. Hundreds of families were deeply grateful for the buyback which had allowed them to move on, Ms Heseltine said.

"Throwing money at an inquiry involving just one jurisdiction would be a waste of resources bordering on scandalous," she said. "The Mr Fluffy issue spans three jurisdictions: the ACT, NSW and the Commonwealth."

Ms Heseltine unsuccessfully sought Labor preselection for the October ACT election.

Liberal Leader Jeremy Hanson has called for a board of inquiry repeatedly and promised to set one up if he wins government in October.

"Mr Barr's excuse about needing a joint inquiry with the federal and NSW governments is disingenuous," he said. "A board of inquiry would be established under the ACT Inquiries Act and would have appropriate powers to run a full and thorough investigation on its own."

A cross-party parliamentary inquiry last year called for a board of inquiry. Mr Barr and Katy Gallagher before him have consistently said an inquiry would be held once the demolition was substantially under way or complete, but both have hedged their bets on a full board of inquiry.

Mr Barr told the Assembly last year "a board of inquiry remains important" but it was a question of when. Last year, he agreed to push for federal support under pressure from the Greens' Shane Rattenbury who said then an inquiry would ensure authorities learned from mistakes and allow victims to have their stories put on the public record.

Senator Gallagher said on Thursday the priority focus must remain on the buyback scheme for Mr Fluffy owners.

"Any future inquiry, in whatever form that might take, should only occur if the Commonwealth government fully co-operates and would have to begin from the time that the Mr Fluffy business began operating in the territory in the late 1960s."