Attorney-General Mark Dreyfus wants to take the final case launched by late land rights champion Yunupingu to the highest court in the country.
In May, a decision by the full bench of the Federal Court paved the way for the Gumatj to potentially receive compensation for bauxite mining at Gove in northeast Arnhem Land.
Mr Dreyfus said on Tuesday that the federal government has filed a special leave application in the High Court to appeal.
In 2019, the late Yunupingu, on behalf of the Gumatj clan, made an application for native title for land in the Gove Peninsula.
He simultaneously lodged a compensation application for the alleged effects on native title of certain executive and legislative acts from 1911-1978.
The case centred around the Commonwealth's decision to allow mining on Gumatj country in 1968 without consent.
Attorney-General Mark Dreyfus said in a statement that he recognised the significant contribution that Yunupingu had made to land rights in Australia but the case raised important legal issues.
"Initiating this landmark case was one of many actions he took to build a better future for his people," he said.
"The application of these constitutional issues in the context of native title compensation is new and the Federal Court decision ... represents the first time these issues have been judicially determined in that context.
"In my view it is appropriate that these critical issues be settled by the High Court so that parties to this and future matters have clarity and certainty about the law in this area."
Yunupingu, who died in April, claimed compensation under section 51 of the constitution, which empowers the parliament to make laws for the acquisition of property on just terms.
That means the Commonwealth can acquire land if the landowner is paid.
The compensation was sought for land from which bauxite had been mined since 1968, when the Australian government entered into a lease with Nabalco.
The mining lease is now held by Swiss Aluminium.
Other Yolngu clan groups, including the Rirratjingu people, have also made claims on parts of the land in question.
Native title is yet to be determined.
