The Federal Government has been forced to replace the head of the royal commission into the Northern Territory's youth detention system, just a week after establishing the inquiry.

Key points: Brian Martin steps down in the "public interest"

Brian Martin steps down in the "public interest" Mick Gooda to stand down as Aboriginal and Torres Strait Islander Social Justice Commissioner

Mick Gooda to stand down as Aboriginal and Torres Strait Islander Social Justice Commissioner Warren Mundine says he is "sad" Mr Martin resigned from the royal commission

Former Northern Territory chief justice Brian Martin was appointed to head the royal commission on Thursday, following the Four Corners report on the treatment of child prisoners in the Don Dale Detention Centre in Darwin.

But Mr Martin has now stepped down, saying he does not have the "full confidence" of sections of the Indigenous community and was not prepared to compromise the inquiry.

The commission will instead be jointly run by high-profile Indigenous figure Mick Gooda and former Queensland Supreme Court judge Margaret White.

Mr Gooda's appointment follows increasing community and political pressure to appoint an Indigenous representative and he will resign from his role as the Aboriginal and Torres Strait Islander Social Justice Commissioner to take the new job.

"I've been fairly vocal about Aboriginal and Torres Strait Islander people needing to have confidence in the process, to have confidence in the outcomes," Mr Gooda said.

Ms White was the first woman to be made a judge of the Queensland Supreme Court and also appeared in the Mabo versus Queensland case.

She said the task ahead would be "rather difficult, if not challenging."

"We hope to a good outcome and some recommendations which will see good juvenile justice in the NT," she said.

Sorry, this video has expired One of the incidents that has sparked the royal commission

Labor accuses Turnbull of 'bungle'

Opposition Leader Bill Shorten had been agitating for an Indigenous co-commissioner to be appointed, and said the Prime Minister had rushed the process in the first instance.

"This is what happens when you rush and you bungle, you create confusion, you create problems and put people into corners," Mr Shorten said.

"Today's announcement could have been avoided if Mr Turnbull had simply learned one lesson — consult, cooperate, achieve consensus by listening to people."

The Prime Minister has defended the quick decision to call the royal commission last week, within 12 hours of the story going to air.

"Australians expected their government to move swiftly and decisively," Mr Turnbull said.

Attorney-General George Brandis said Mr Martin decided to step aside on Saturday, and it was not something the Federal Government asked him to do.

"In our view it was not necessary for him to stand aside. Notwithstanding that, he made a firm decision," Senator Brandis said.

Outspoken Gooda steps back from Giles criticism

In the wake of last week's Four Corners story Mick Gooda had called for Malcolm Turnbull to sack the Northern Territory CLP Government.

He has since walked back from that remark.

"Tuesday, you know, was a day of emotions and people had all sorts of emotional responses," he said.

"In the clear light of day I probably wouldn't think that."

Mr Shorten also defended the comments.

He said "there are a lot tougher things being said about the Giles Government than what Mr Gooda said."

Martin defends decision to walk away

Mr Martin said his decision to step aside did not mean he accepted claims he had a conflict of interest because of his previous role as an NT judge.

"My resignation does not imply that I doubt my capacity to be both independent and competent in the role of the commissioner, nor does it imply that I accept that there is or would be a reasonable apprehension of bias," he said.

He also acknowledged he did not have the faith of some Indigenous groups central to the royal commission.

"It has become apparent that, rightly or wrongly, in this role I would not have the full confidence of sections of the Indigenous community which has a vital interest in this inquiry," he said.

"As a consequence the effectiveness of the commission is likely to be compromised from the outset.

"I am not prepared to proceed in the face of that risk."

Mr Shorten had called for the appointment of an Indigenous commissioner, which Mr Martin said would have some advantages.

"But, whichever way it goes, it is incorrect to suggest that someone who is not Indigenous could not conduct this properly and effectively, provided that person consults and gets advice on those specialised issues," he said.

Martin 'wimped out', Mundine claims

The head of the Prime Minister's Indigenous Advisory Council, Warren Mundine, told triple j's Hack that Mr Martin "wimped out."

"To be a royal commissioner you've got to be tough, you're going to deal with some very serious issues … You're looking at criminality, there could be charges, there's going to be whole range of things come out of this royal commission," Mr Mundine said.

"There's going to be people not happy, people abusing him, and it's going to be a tough job."

However, he said Mr Martin did not need to resign.

"He just needed to work with the Government and move forward. But that's his call," Mr Mundine said.