The ACT and federal governments have agreed to share costs of a fund to help cover medical expenses for Canberrans who contract the incurable disease in the future.

The ACT government, which will run the scheme, has made clear it is not a compensation fund, insisting that setting it up was the "right thing to do ... not a legal solution".

Marion McConnell and Paula Blandford both lost their husbands to mesothelioma, which they're believed to have contracted after living in Canberra homes contaminated with loose-fill asbestos.

Mrs McConnell, whose husband Brian died in June 2016, said she was "pleasantly surprised" when news of the fund broke on Thursday night.

But she admits her "heart sank a little bit", as it hit home that no such support or recognition had been there after her husband was diagnosed.

"I have a bad feeling that my husband is not being acknowledged, [nor] the other that people are already dead from this," she said.

"Words [of acknowledgement] would help a lot."

Mrs McConnell said the new fund would provide some comfort and relief to families given that some life-prolonging treatment, in particular the immunotherapy Keytruda, cost thousands of dollars for each round.

But she warned the financial support would not "ease the suffering".

Mrs Blandford, whose husband Nicholas died in December 2019, echoed those sentiments.

"Whatever the government does they will never compensate us, we will live with this ongoing pain," she said.

Mrs Blandford was pleased the ACT and federal governments were finally taking responsibility for the crisis - even if it has come too late for her.

She believes that had the government refused to allow her family to renovate their Curtin home in the late 1980s, her husband would still be alive.

"I'm relived that the government is accepting responsibility," she said.

"But they have a long way to go to actually compensate us for the uncertainty. We lived under the shadow of this uncertainty and worry.

"The rest of the people out there need to know about the tragedy that has been inflicted on us."

The federal government on Thursday announced it would contribute up to $8 million toward the ACT-run fund, following months from advocacy from family and friends of mesothelioma sufferer James Wallner.

The Barr government will match the Commonwealth's contribution, meaning up to $16 million could be available to future sufferers.

Mr Barr said full details about the scheme would be announced in the coming weeks.

The ACT government has, however, moved to clarify that its decision to establish the scheme does not mean it has accepted legal liability for the health impacts of Mr Fluffy asbestos.

An admission of liability - either from the ACT or Commonwealth - could open the door to compensation claims in the courts.

"The government is setting up the fund to support sufferers at a difficult time and to give them confidence that their families will be supported after their passing," Mr Barr's spokeswoman said.

"The support fund is not designed as compensation to resolve legal liability, it's the right thing to do for ACT residents, not a legal solution.

"The ACT government has consistently made clear that it holds no legal liability for the action or inaction of the Commonwealth government relating to Mr Fluffy pre self-government."

Health Minister Greg Hunt did not respond directly when asked if the Commonwealth's contribution to the scheme was an acknowledgement of its responsibility.

Mr Hunt's spokesman said it was not appropriate to comment on details of the fund until it had been finalised.

"The ACT government has provided proposals to the Commonwealth and in light of the urgency and compelling circumstances of some victims of non-occupational asbestos exposure, the Commonwealth has moved quickly to again work with the ACT government to provide financial support to affected citizens," the spokesman said.

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