A second Aboriginal man has been released from immigration detention and another 23 cases are “under review” after the high court decision that Aboriginal people are not aliens for the purpose of the constitution and cannot be deported.

“We are working through the cases that might fall within that remit,” the home affairs department secretary, Mike Pezzullo, told a Senate committee on Monday.

“A number of persons have come forward and advised on potential claims” and the department is “working on it as quickly as possible”.

There is a three-part definition of Aboriginality accepted by the high court in the Mabo cases: biological descent, self-identification and recognition of identity by a First Nations group. The court said the tripartite test put Indigenous Australians beyond the reach of the aliens power in the constitution.

The majority of the high court ruled that New Zealand-born Brendan Thoms was not an alien and the commonwealth did not have power to deport him. He was released from detention in early February.

A further hearing will decide if the second plaintiff, Daniel Love – who was born in Papua New Guinea – is a Gamilaraay man.

Both men were convicted of criminal offences and served time in prison. When their sentences ended in 2018 they both had their visas revoked and were taken to immigration detention in Brisbane for deportation.

General counsel to the home affairs department, Pip de Veau, told the Senate committee on legal and constitutional affairs that another person in detention had met the test and was released last week, but “there is no one else in the visa stream close to establishing the credentials required”.

De Veau confirmed there were 23 cases in which “negotiations are ongoing to establish evidence” but they include “all possible indications of Indigeneity, not those that ultimately might meet the threshhold”.

“The bulk of those we already had information about prior to Love and Thoms, and a small number have self-identified since the decision,” she said.

Last month the attorney general, Christian Porter, said the government was looking to legislate another way to deport the “not very large” group of Aboriginal non-citizens who had committed crimes.

“People who are born overseas, who aren’t Australian citizens, but may be able to show Indigeneity and who are in Australia on a visa and commit an offence” would now “have to be treated differently from all other persons in the same circumstances” because they could not be deported under existing law.

“And we’ll be looking into ways in which we might be able to effect that policy,” he said.