Northern Territory MP Marion Scrymgour said a criminal investigation was a job "only police can undertake" but it did not have to be conducted by NT detectives when federal police could step in.
Her call comes amid growing pressure for an independent investigation into the death of mentally disabled man Kumanjayi White on May 27.
He died shortly after being forcibly restrained by two plain-clothes police officers in a supermarket in Alice Springs.
Police allege the 24-year-old, originally from the outback community of Yuendumu, was shoplifting and had assaulted a security guard who confronted him in the confectionery aisle.
NT Police and Chief Minister Lia Finocchiaro have strongly rejected calls for an external investigation, saying police are the right authority to carry out an investigation coupled with a coronial inquiry.
Ms Scrymgour, the federal member for Lingiari, said at the end of the day it had to be a police decision whether to lay criminal charges.
"But it doesn't have to be NT Police officers who undertake the task," she said in a statement.
Having the AFP take over would extract NT detectives from a role which would subject them to scrutiny and criticism as well as enable the Yuendumu community to have full confidence in the process, the MP said.
"Just as happened during the COVID lockdown period, police officers from outside the NT can be brought in."
Meanwhile, outspoken senator Lidia Thorpe said Friday marked five years since the global Black Lives Matter mobilisation sparked by the police killing of George Floyd in the US, with an officer's knee on his neck.
"Kumanjayi White died the same way," she said in a statement on Thursday, citing an eyewitness account of the supermarket incident.
"Since the Royal Commission into Aboriginal Deaths in Custody in 1991 at least 595 of our people have died in custody ... and not a single police or prison officer has ever been held criminally accountable," the senator said.
On Wednesday evening, hundreds of people attended a candle-lit vigil outside the NT parliament in tribute to Mr White and to support his grieving desert community.
A large banner stating "We stand with Yuendumu" was displayed in front of the parliament's entrance while another banner laid on the ground read "Justice for White".
Organisers invited people to light candles or lay flowers following speeches highlighting the mistrust of police in Aboriginal communities and the need for an external inquiry into Mr White's death.
Justice Not Jails spokesperson Jade Richie said "no police should be investigating police" in a death-in-custody case.
Her group is organising a "national week of action" in response to Mr White's death, with vigils planned across the country.
The Yuendumu community also lost 19-year-old Kumanjayi Walker in 2019 when he was fatally shot by then NT police officer Zachary Rolfe during a bungled arrest.
Mr Rolfe was in 2022 found not guilty of all charges over the death.
The Kumanjayi Walker coronial findings have been postponed until July 7 after Kumanjayi White's death in custody.
Federal Indigenous Australians Minister Malarndirri McCarthy said on Thursday an independent death in custody probe might be warranted "in the interest of having some separation".
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