Dutton has made it clear the youth will be deported.
"We will make sure that he's deported at the first available opportunity but at the moment he's delaying his return to New Zealand," he told reporters recently.
The minister has the power to overrule the AAT's decision.
The Department of Home Affairs can also appeal against an AAT decision in court.
The youth has lived in New South Wales with his family for the last seven years and was to have been deported under Section 116 of the Migration Act, which provides for deportation where someone on a visa is deemed a potential risk to the community.
Acting Deputy Prime Minister Winston Peters weighed in on the case recently, saying Australia was breaching the UN Convention on the Rights of the Child.
He said today the release was good news and the youth was being taken back to his family in NSW.
"I hope he uses this chance to turn his life around," Peters told Radio NZ.
Justice Minister Andrew Little, who along with Peters will appear in a story about deportations on the ABC's Foreign Correspondent current affairs programme tonight, told the Herald deportation was the ultimate restriction on liberty.
"When a minister or a government department is left to make a decision like that there have to be proper processes for appeal and review. In the interests of the rule of law,and because it is a very human decision, there should be multiple levels of appeal.
"I would be concerned if in this case, and in any case, that there aren't those avenues of appeal that allow for multiples levels of review of a decision that has such far-reaching consequences."
Little said it appeared that in these deportation cases there were limited rights of appeal and Dutton had an ultimate right to make a decision that could not be reviewed.
He said every country could make its own rules but they were all part of the global community and some signed up to international agreements, standards of conduct and the rule of law.
"When the state exercises powers that encroach on individual rights, particularly as draconian as removing someone from a country and preventing them from ever returning, you exercise those powers with considerable care and with considerable oversight.
"If that isn't happening in these cases then that is a matter of concern," Little said.
Dutton told Foreign Correspondent every nation, including New Zealand, exerted its own right to deport criminals.
"They're New Zealand citizens, they're not Australian citizens. And it's no breach of human rights," he said, according to an ABC report.
