The former prime minister joined filmmaker Rachel Perkins and historian Henry Reynolds to discuss whether the conflict can be considered warfare and how it should be treated in the nation's memorial.
"Obviously we want Aboriginal Australians to have just as much a sense of ownership over the war memorial as anyone else," Mr Abbott told the AWM's Through Their Eyes podcast, released on Thursday.
"I think that the story ... does need to be told. It's a question of where it is best told. Now, I think there should be an acknowledgement of it here at the war memorial, but I don't think this is the place to dwell on it."
Professor Reynolds said a properly funded separate museum of frontier conflict run by the Institute of Aboriginal Affairs would be a good idea.
Mr Abbott, a former council member of the memorial, said he supported the proposal.
"It is important that we familiarise ourselves with the true history of our country, and frontier conflict is certainly a significant part of that ... let's do it," he said.
Ms Perkins, an Arrernte and Kalkadoon woman, argued the conflicts constituted warfare.
"It may not appear as war in the same way as it has been quantified at Vietnam and all those other theatres of war that you described, but it's the nature of the things that it was fought over, not the way it was fought," she said.
"It was fought over our lives, our livelihood, our culture, and our land."
The debate about how frontier conflict is represented comes following the $550 million expansion of the Australian War Memorial.
The war memorial's council chair Kim Beazley said frontier wars had been a standard part of the teaching of Australian history for some time.
The war memorial will in September hold a conference on Australia's first wars to debate the issue, in addition to the nation's 19th century military history.
"The time has come for us here at the Australian War Memorial to give what is already in the galleries a stronger interpretive presentation of our beginnings, and this conference will provide us with important guidance," Mr Beazley said.
Professor Reynolds also pointed to official correspondence by soldier and colonial administrator George Arthur who mentioned war about 20 times.
"For a soldier who had seen war, what was happening in Tasmania was war," he said.
In response, Mr Abbott said: "This was in a sense of tragedy. The question is, was it an atrocity? I don't think we can reasonably say it was."
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