Northern Territory Chief Minister Lia Finocchiaro has criticised two senior Indigenous Labor politicians, saying they "should know better" for calling for an independent investigation into the death in custody of 24-year-old Warlpiri man Kumanjayi White.

Mr White, who had strong connections to the Yuendumu community, was under state guardianship and living in supported accommodation when he died after being restrained by two plain-clothed NT Police officers following an alleged altercation at a Coles supermarket.

His death has prompted protests across the country — including in Naarm/Melbourne, Sydney, Magandjin/Brisbane, Darwin, Boorloo/Perth, Wollongong and Mparntwe/Alice Springs —with calls from Mr White's family, legal advocates, land councils, and human rights organisations for an independent investigation.

Those calls have been rejected by both NT Police and the Chief Minister.

Among those urging an independent inquiry are Minister for Indigenous Australians, Malarndirri McCarthy, and Member for Lingiari and Special Envoy for Remote Communities, Marion Scrymgour.

Responding to questions at budget estimates in NT Parliament on Tuesday, Ms Finocchiaro — who previously described Senator McCarthy's remarks as "uneducated" and "unhelpful" — doubled down on her criticism.

"The comments being made by federal members of parliament are quite frankly appalling," Ms Finocchiaro said.

"This is a sad time for the community; our police have an incredibly important job to do, and the politicisation of this issue helps no one. It does not support our police or the Coroner to do their work, or the families who are grieving and communities who want answers."

National Indigenous Times has contacted Ms Finocchiaro for clarification on who she means by "no one", as Mr White's family, along with their legal team and several Aboriginal organisations, continue to advocate for an independent inquiry.

Their concerns centre on a lack of police oversight and a documented history of racism in the NT Police.

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Last week, Ms Scrymgour called for the Australian Federal Police to take over the investigation into Mr White's death.

Independent Senator Lidia Thorpe also condemned the NT Government's handling of the case, accusing it of a "cruel, punitive approach to law and order," and said its policies have become the subject of human rights complaints.

"The NT government and NT police are not up to the job and do not have the trust of the community," she said.

Ms Finocchiaro — who Senator Thorpe described as "out of her depth" — has led a government accused of ignoring Indigenous voices while pursuing hardline law and order policies. Nevertheless, the Chief Minister stood by her criticism of Senator McCarthy — who the PM revealed on Tuesday had lost her father over the weekend — and Ms Scrymgour.

"They have been members of parliament for a long time at both the Territory and federal level; they should know better," she said.

"I urge all people with a voice and power to influence to use it for good and reinforce the strengths of our institutions, particularly the Northern Territory Police Force which investigates matters and supports the Coroner."

First Nations people in the NT have long raised concerns about policing. In 2024, NT Police Commissioner Michael Murphy issued a public apology to Aboriginal Territorians for "the past harms and the injustices caused by members of the Northern Territory Police."

Speaking on ABC News Breakfast on Monday, Mr White's grandfather, Warlpiri Elder Ned Jampijinpa Hargraves, said a meaningful apology was still needed.

"You want to say sorry? You take the belt off, take your guns off," he said.

"I would say this [to the police]: 'Get off our back … get off our back.'"

In a statement released over the weekend, George Newhouse — Chief Executive of the Sydney-based National Justice Project — also criticised the NT government's refusal to allow an independent investigation.

"The family has called for these investigations to be independent, but this demand has been unjustly rejected by Northern Territory Chief Minister who continues to oversee a racist agenda against the NT's Indigenous peoples," he said.

"Now that a criminal investigation is underway, the family call on the Northern Territory police officers involved to be stood down immediately. This should be an obvious action in any criminal inquiry. Stand down now."

Despite the mounting pressure, Acting NT Police Commissioner Martin Dole told estimates that the case could not simply be handed to another authority.

"If we were to bring in an independent investigator, they would have to be sworn in as members of the Northern Territory Police Force to utilise our powers under the Act," he said.

However, during unrest in Alice Springs last year, NT Police swore in South Australian Police officers under the same provision. National Indigenous Times has sent questions to NT Police asking what the difference between the two situations is.

Last week, National Indigenous Times also revealed that none of the officers involved in Mr White's arrest had been stood down. When asked why, Acting Commissioner Dole said that the decision fell to the Professional Standards Command.

"Just because a matter sits in the current realm of a criminal investigation, does not necessarily dictate that a member would be stood down," he said.

"It depends on how much evidence is available and what stage the criminal investigation reaches before that decision is made, in conjunction with Professional Standards Command."