Human Rights Commission president Gillian Triggs said Mr Gooda was the best man for the job.
"I think, as he said himself, people reacted so strongly to those pictures that they were emotional responses," she told ABC TV.
The prime minister has resisted calls for the royal commission to cast a wider net and examine alleged abuse cases in other states.
Instead Malcolm Turnbull will put the issue of juvenile detention and indigenous incarceration on the agenda at the next meeting of federal, state and territory leaders later this year.
Professor Triggs said it made sense to deal with the immediate NT problem first, wait for recommendations and then look at some form of national inquiry down the track.
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