Special Minister of State Scott Ryan says the Coalition has ruled out appointing two Indigenous Australian co-commissioners to the royal commission into the Northern Territory's juvenile justice system.

Prime Minister Malcolm Turnbull set up the royal commission this week after Four Corners aired vision of boys in a Darwin detention centre being teargassed and forcefully stripped naked.

Senator Ryan said the Government would not be acting on the Opposition Leader Bill Shorten's suggestion for two Indigenous Australians to work alongside the royal commissioner, Brian Martin.

"The Government has appointed Brian Martin and we are keen that this royal commission get underway very quickly, that's why it's so targeted," Senator Ryan told Sky News.

Former human rights commissioner turned-Liberal MP Tim Wilson told Sky he wanted a parliamentary inquiry.

He said it could look into broader issues, including the high incarceration rate for Indigenous Australians and West Australian Premier Colin Barnett's suggestion to strip the NT of responsibility for youth justice.

Inquiry will be seen as a 'con job': Shorten

Mr Shorten made his call for two Indigenous co-commissioners during a visit to Darwin yesterday.

"This royal commission has to be with Aboriginal people, not to Aboriginal people," Mr Shorten said.

"I believe it would be appropriate for the royal commission to have two co-commissioners who are Aboriginal Australians, strong people, men and women, who can make sure the voices and the experiences of Aboriginal Australians are given full justice in this royal commission."

Sorry, this video has expired Royal commission: Shorten calls for Indigenous co-commissioners to achieve 'full justice'

Mr Shorten also went on to say having a royal commission without Aboriginal co-commissioners would be seen as a "con job" — but the phrase was left out of the official transcript distributed by his office.

"To have an inquiry on the treatment of Aboriginal children in the justice system in the Northern Territory and not have Aboriginal co-commissioners will be seen as a political manipulation," the transcript reads.

But Mr Shorten's full quote was: "To have an inquiry into the treatment of Aboriginal children in the criminal, in the justice system in the Northern Territory and not have Aboriginal co-commissioners will be seen as a con job, seen as a political manipulation."

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Senator Ryan has described Mr Shorten's use of the phrase as "confected outrage".

"I don't think it's particularly appropriate language to use given the seriousness of the events and given the genuine spirit in which the Government has acted … and I don't think it achieves what I think every Australian wants here, which is a real commitment to finding out what happened and ensuring it doesn't happen again."

"Bill Shorten also used the word con job yesterday, and quite frankly, Bill Shorten's confected outrage on a daily basis on some issues is a bit like a grey sky in Melbourne in July, you just have to get on with the job and ignore it."

The Opposition Leader has not backed down from his use of the phrase.

"I'm reflecting what Aboriginal people are telling me," Mr Shorten said at the Garma Festival in north-east Arnhem Land on Sunday.

"At the end of the day I want the royal commission to be successful.

"Why should Australians settle for second best when we've got a terrible juvenile detention system at the excesses that we've seen?"

Giles is 'incompetent' and should be subpoenaed: Dodson

Labor Senator Pat Dodson said the Northern Territory's Chief Minister Adam Giles should give evidence before the Royal Commission, saying the NT Government should not be involved in setting up the royal commission.

"The Chief Minister of the Northern Territory has demonstrated he's incompetent to deal with this matter and I don't think he should be in any way influencing it," he said.

"He should be subpoenaed to appear before it."

Speculation Giles could replace Scullion

Coalition MPs and Senators have privately speculated for some time that Mr Giles may replace Senator Scullion in the Senate after the NT election.

Senator Dodson said that "would be an absolute travesty of justice."

Asked if Senator Scullion had any comment to make about the speculation, his spokesman released a short statement.

"Senator Scullion has been asked variations of this question on numerous occasions and the answer has always been the same: no," the spokesman said.

Coalition MPs believe Mr Giles's chances of replacing Senator Scullion have been weakened, with the NT Government expected to be defeated at next month's election.