A grassroots community organisation has renewed calls for an independent investigation into the death of 24-year-old disabled Warlpiri man Kumanjayi White in police custody, saying the Northern Territory Police's "long-standing and well-documented patterns of racial discrimination" make internal investigations untrustworthy.

Justice not Jails, a group formed in opposition to the NT Government's "racist 'tough on crime' agenda," said last week's refusal by Acting Police Commissioner Martin Dole to support an independent probe into the death was unacceptable.

They argue only a fully independent inquiry would ensure accountability and justice.

"NT Police's repeated use of internal investigations, despite long-standing and well-documented patterns of racial discrimination, is not transparent nor trustworthy," the group said in a statement.

They also called for the immediate release of CCTV footage to the family and urged police, media, and the public to stop vilifying Kumanjayi White's character.

Justice not Jails' statement follows public comments by NT Police alleging criminal behaviour by the young man, despite not commenting on allegations Kumanjayi was forcibly restrained and an officer placed their knee on the back of his head.

Warlpiri Elder and grandfather of Kumanjayi, Ned Jampijinpa Hargraves, condemned police for publicly framing his grandson as a criminal before the investigation concluded.

"It is disgraceful that police are already putting out stories that portray my jaja (grandson) as a criminal," Mr Hargraves said.

"We are always told by lawyers that we need to wait for investigations to take place before we comment on events."

North Australian Aboriginal Justice Agency (NAAJA) founder, Natalie Hunter, echoed calls for an independent inquiry, saying the NT Police have a "known history of racism and abuse" and cannot be trusted to investigate themselves.

"Black lives matter," she said.

"The family needs to be empowered to ask the questions they want answered on their own terms, and the police need to step out of the way and let them do that."

Human rights advocate Thomas Mayo also backed the calls for an external investigation, saying: "A mere glimpse at the record of police investigating themselves when there are allegations of racial violence against them is enough to understand why the family and community are calling for an independent investigation."

"I ask anyone with a sense for fairness and justice to loudly support the family of Kumanjayi White and their demands," he said.

In a statement last week, Mr Hargraves said he was "angry and frustrated that yet another one of our young men has lost his life at the hands of the police".

"We are demanding answers and justice. We know that he was held down by two police until he lost consciousness and perished. But at the moment, we are in the dark about what really happened," he said.

"What are the police doing using such force on a vulnerable young man in a supermarket? Did they even try to de-escalate?"

Kumanjayi, who was living in supported accommodation under state guardianship due to his disability, died last Tuesday after being restrained by two plain-clothed officers during an alleged altercation with a security guard.

Police said they "restrained the adult male" after the altercation at an Alice Springs Coles; however, the male "stopped breathing and CPR was commenced".

He died 70 minutes later.

Witnesses to the incident say they saw an officer with a knee on the back of Kumanjayi's head. Others have told National Indigenous Times he was allegedly placed in a headlock by a security guard.

Despite growing pressure, the NT Police have not confirmed what restraint was used or how someone being "placed on the ground" can lead to their death.

Police Prosecutor Steven Haig is reportedly one of the officers involved.

Questions have been submitted to NT Police about whether he will continue in his role while under investigation.