Aboriginal Australians are exempt from immigration law, the country's top court ruled Tuesday, in a historic decision that found indigenous people born overseas cannot be deported.

Australia had been trying to deport two men - Papua New Guinea citizen Daniel Love and New Zealand citizen Brendan Thoms - under laws that allow a convicted criminal's visa to be cancelled on character grounds.

Both men identify as Aboriginal Australians, each has one indigenous parent, and they have lived in the country since they were small children.

Love, who served time for assault, and Thoms, who had been jailed for domestic violence, have been battling in the courts to stay in Australia, arguing that they may be "non-citizens" but they are also not "aliens".

The High Court ruled in a decision that split the judges 4-3 that Aboriginal Australians "are not within the reach" of constitutional provisions relating to foreign citizens.

Indigenous people have inhabited the vast continent for more than 60,000 years, while the modern nation's constitution only came into force in 1901.

Thoms - who was already recognised as a traditional land owner - was accepted by the court as Aboriginal. But the judges could not agree on whether Love was under a three-part test that considers biological descent, self-identification and community recognition.