Allegations surfaced this week of mistreatment of children involved in the Many Colours 1 Direction program and on the identity of its founder Allan Brahminy.

Mr Brahminy has claimed he was adopted by an Aboriginal family after he was abandoned on a riverbank as a baby.

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This claim has been labelled a fabrication by some who had formerly been close to him.

They have said his real name is Allan Stauffer and his late biological mother was very much part of his life.

Human Services Minister Roger Jaensch on Friday said a review of Mr Brahminy's program would be completed by the end of the month.

He said child safety staff over the past few weeks had reported that the six young Tasmanians involved in the program were safe, well, and had made good progress in the program.

"They want to stay there," Mr Jaensch said.

"While I have asked my department to investigate all of the new allegations that have been raised as a matter of urgency ... there is evidence that this program is achieving results for these kids where other programs have failed them in the past.

"I need to be very careful that I don't take any knee-jerk reaction to any media report or the demands of our political opponents to step in in a way that would jeopardise the progress that those kids are making in the program."

He said background checks by the government on a provider focused on their history in a particular sector and police record, not their heritage.

Mr Jaensch said it was up to Mr Brahminy to answer questions about his heritage.

Labor's child safety spokesman Josh Willie said the government had a responsibility to ensure allegations about his identity and background were investigation.

"The state government is essentially acting as a parent to these children and, while the allegations remain untested, it has a responsibility to bring them home," he said.

"If it was a teacher or another professional responsible for looking after young people, they would be stood down while an investigation took place.

"It is beyond time for this incompetent minister to go.

"His position is untenable and if he won't go voluntarily, the Premier must step up and sack him."

Greens justice spokeswoman Rosalie Woodruff said it was not good enough for children to be kept in the Northern Territory while questions remained unanswered on the program and Mr Brahminy himself.

"The minister much take responsibility for the care of those vulnerable children and bring them back to Tasmania so they can be under the independent eyes of the Children's Commissioner and in a place where we can guarantee their safety," she said.

"The minister can't say unequivocally that the children there aren't being mistreated."

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