Liberal senator Andrew Bragg is among politicians calling for funding for the National Resting Place project to be included in this month's mid-year economic review.

The Canberra Times can confirm the government has been handed the detailed business case for the long-awaited Ngurra Cultural Precinct, which would hold the repatriated ancestral remains of Indigenous Australians.

The idea has been on the agenda for more than eight years, with a federal parliamentary inquiry in 2019 recommending a resting place be built as part of a relocation of the Australian Institute for Aboriginal and Torres Strait Islander Studies (AIATSIS) to a new site in the heart of Canberra.

The federal budget in May allocated $4.7 million for a study to scope possible sites, estimate the project's cost and consider what other components the development might include.

A National Indigenous Australians Agency spokesman confirmed the business case had been completed, but said it couldn't share details of its findings while they were being considered by the government.

Healing Foundation chief executive Fiona Cornforth is among the supporters pushing for the project to be funded and built.

She said a resting place would help address a lack of understanding in the broader community about the trauma associated with acts of colonisation, including how Indigenous people had in the past been seen "as objects of study that should be taken overseas".

"What a memorial will do it, if it's in the nation's capital with all of the other monuments that our young people are supported and funded to visit each year, is that our rising generation will understand where we are at as a nation in terms of addressing and resolving our burden of trauma," she said.

The project has support within Coalition and Labor ranks.

Senator Bragg said he and several colleagues had asked Treasurer Josh Frydenberg to fund the project in the government's mid-year economic update, which will be handed down later this month.

"The Parliamentary Triangle has a hole in its heart without a building which recognises Australia's Indigenous heritage," he said.

"In the nation's capital we make space to show our pride in arts, democracy, history and war veterans - but we are bereft of something specifically designed with, and for Indigenous Australians."

Labor MP for Bean David Smith, who sits on the committee which oversees the Parliamentary Triangle, said with the business case finalised there was no need for further delays on a project which has bi-partisan political support.

"It is now time to get moving on something that is part of our journey towards reconciliation," he said.

The Canberra Times contacted the offices of Mr Frydenberg and Minister for Indigenous Australians Ken Wyatt, but did not receive a response.

Meanwhile, the proponents of a separate Indigenous cultural centre on the banks of Lake Burley Griffin are understood to be still pushing for government support to get the $150 million project off the ground.

The private backers have previously asked the government to contribute $50 million and surrender the car park between the National Library of Australia and Reconciliation Park, where they hope to build their hi-tech National Dreaming Centre.

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