The inquiry into last week's death in custody will be headed by Philip Moss, a retired anti-corruption chief who last year produced a damning report about rape and abuse inside the Nauru detention centre.

Barrister Bernard Collaery, a former ACT attorney-general, is also now acting for the family, and has called for an independent, proactive probe into the cause of Mr Freeman's death.

"Whether we're having an inquiry or an inquest, the public interest is so great that the measures taken at the outset must be proactive," Mr Collaery said.

"These regrettably include a wholly independent autopsy by an eminent expert."

The circumstances of Mr Freeman's death are still unclear.

Justice Minister Shane Rattenbury has promised the prison's books will be open to Mr Moss, that he will have "free rein", and that his findings will be made public.

Mr Rattenbury acknowledged the distress that the death had caused the family and the broader Indigenous community in the ACT.

"No death in custody is acceptable," he said.

"We need to work very hard to prevent this, and that's why we're taking this very seriously."

Fellow Indigenous inmates are also being offered additional support and counselling.

But Mr Rattenbury rejected any conclusion at this early stage that the death was preventable, given the cause of death has still not been formally established.

"There has been no finding yet of the cause of death. I don't think you can make those connections at this point in time," he said.

"I will not be jumping to any conclusions."

Mr Freeman was viciously bashed in a near-fatal attack in his prison cell within hours of arriving at the Alexander Maconochie Centre last year. He had been housed with sentenced prisoners, something that authorities try to avoid, particularly in a human rights-compliant jail like the AMC.

Police investigated that assault, but struggled to get witnesses to speak, and did not lay charges.

The severity of his injuries and ongoing threats to his safety prompted Aboriginal Legal Service lawyers to fight desperately to have him released on bail, arguing he was likely to die if he remained inside.

There was evidence of further risks to his safety and of threats of self-harm.

Authorities assured the court that prison was the safest place for Freeman, and magistrates feared he would reoffend if released. One feared he would become a "one-man crime wave".

The inmate died last week, prompting anger within the Indigenous community and from Freeman's family.

Mother Narelle King said last week that the justice system had failed her son.

"My son was never a violent man. He just stole a few cars," she said.

On Thursday, Justice Minister Shane Rattenbury revealed the six terms of reference for the independent inquiry, which will run additionally to the standard coronial inquiry for a death in custody and a police investigation.

Mr Moss has been tasked with assessing the "adequacy of the management, care, and custody" of the detainee, the overall effectiveness of induction and risk assessment at the jail, the separation of vulnerable detainees, the adequacy of information sharing, and the accessibility of health and other support services.

The inquiry is expected to be completed and a report provided to Mr Rattenbury by August 31.

"I would like to take this opportunity to reiterate my deepest sympathies to the family and friends of Steven Freeman and again ask that their privacy be respected," Mr Rattenbury said in a statement.

"I am mindful of the effect this death in custody may have on other detainees in the AMC, particularly those that identify as Aboriginal or Torres Strait Islander. ACT Corrective Services has put in place a number of measures to assist detainees in this difficult time."

Mr Rattenbury said some Indigenous inmates had asked to go to Mr Freeman's funeral, and he said that would be facilitated.