The new Federal Government has abandoned its predecessor's attempt to restore the Commonwealth's power to deport Aboriginal people who are not citizens of Australia.

In February 2020, the high court ruled Daniel Love, born in New Zealand and a member of the Gunggari nation, and Brendan Thoms, a Kamilaroi man who was born in Papua New Guinea, could not be "aliens" under the law because of their Aboriginal heritage and could not be detained and deported under the immigration minister's powers.

The pair had faced the threat of deportation since failing their migration character tests by serving time in Australian prisons.

However, it was revealed by Guardian Australia in October 2021 the Morrison Government was attempting to overturn that ruling, launching a case to restore the minister's powers to detain and deport non-citizen Indigenous people.

The Morrison Government challenged the case of Shayne Montgomery, a New Zealand citizen culturally adopted and recognised by Elders as member of the Mununjali people, to overturn the precedent.

In June, Greens senator and DjabWurrung, Gunnai, and Gunditjmara woman Lidia Thorpe and Larrakia legal academic Eddie Cubillo urged the new Labor government to abandon the case.

On Thursday, Attorney General Mark Dreyfus dropped the proceedings.

The decision will mean at least 12 Indigenous non-citizens who had been at risk of deportation will be able to stay in Australia.

It is the third major move by Mr Dreyfus this month.

On July 7 the attorney general discontinued the prosecution of Timor-Leste whistleblower Bernard Collaery, known as "Witness K", under section 71 of the Judiciary Act 1903.

On Wednesday, Mr Dreyfus tabled the Australian Human Rights Commission Legislation Amendment (Selection and Appointment) Bill 2022, which aims to ensure all future appointments to the Commission are made through a merit-based and transparent process.