A refugee who may have played a part in a people-smuggling operation in which more than 300 people died has lost an appeal to have his case referred to the Minister of Justice.

Maythem Kamil Radhi, 40, was allegedly involved in the 2001 smuggling of a boat-load of people from Indonesia seeking asylum.

The Indonesian boat was headed for Australia but 353 people drowned when it sank off Indonesia after it started leaking.

Radhi, his wife and two children came to New Zealand as refugees in 2009 on the grounds of religious persecution in their native-born Iraq. A third child was born in New Zealand. The family lives in Auckland.

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When Australian federal police realised Radhi was in New Zealand they applied in 2010 to have him extradited to face people-smuggling charges in Australia.

Radhi was arrested in 2011 and has been fighting the extradition process, most recently appealing a decision by the Manukau District Court not to refer the case to the Minister of Justice who could deny the extradition.

In the Court of Appeal his lawyer Lewis Turner argued an extradition would inflict undue suffering on Radhi's children.

If their father was in Australia for longer than two years he could lose his New Zealand visa and might never be able to return to New Zealand or see his children, Turner argued.

Clinical psychologist Dr Barry Eric Kirker, who has interviewed the three children, gave evidence that the two daughters in particular were vulnerable and would be negatively affected by Radhi's extradition.

In court documents Radhi said his family would be torn apart by the move, and his wife and children would be forced to rely on friends in Auckland and social welfare to survive.

But Justice Forrie Miller dismissed his appeal yesterday, saying there were not sufficiently "compelling or extraordinary" circumstances to justify referring the case to the Minister.

The judge accepted that the affect on the children may be severe, but said the extradition would not be unusually "unjust or oppressive" compared to other extradition cases.

Two other people involved in the people-smuggling operation have been tried and convicted in Egypt and Australia, and have been sentenced to prison. Radhi denies any involvement.