Attorney-General Christian Porter is looking "very closely" at a High Court ruling that blocked the government from deporting two Aboriginal men for failing its immigration character test, signalling that a further attempt to remove them may be possible.

In a majority decision, the High Court on Tuesday ruled the government could not rely on the naturalisation and aliens power in the Constitution to deport the two men, who are not Australian citizens but are Indigenous, because Aboriginal people cannot be classified as "aliens".

The High Court of Australia in Canberra Credit:Fairfax

Mr Porter said the decision had implications for the government's policy of deporting non-citizens who committed serious crimes while on a visa and "we'll be looking into ways in which we might be able to effect that policy, without reliance on the power that we previously were relying on".

"These two individuals were not Australian citizens," he told a Perth radio station on Wednesday.