A refugee fighting Australian attempts to have him extradited after more than 350 people died in a people-smuggling accident has taken his case to the Supreme Court.

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

The boat, known as Siev X (Suspected Illegal Entry Vessel X), was sailing for Christmas Island but about 353 men, women and children drowned when it began taking on water and sank off Indonesia.

The Australian Federal Police want to try Radhi for people smuggling, alleging he helped the asylum seekers sail to Australia in a leaky boat.

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The native-born Iraqi denies the allegations.

Yesterday in the New Zealand Supreme Court at Wellington, Radhi's lawyer Ron Mansfield argued that if his client was sent to Australia for more than two years of court proceedings and a trial he would lose his New Zealand residency and be unable to return to his family.

Radhi's Supreme Court appeal comes after he previously lost appeals in the three lower courts - district, high and appeal.

Radhi applied to the District Court on February 27, 2015, for an order referring his case to the Minister of Justice. The minister has a wider discretionary power under the Extradition Act, not available to the courts, to refuse an Australian extradition request.

In a July 3, 2015, judgment, the District Court turned him down.

After further appeals to the high and appeal courts, Mansfield now argues the courts erred in holding that it would not be unjust or oppressive to extradite his client.

Any imprisonment in Australia could leave Radhi in "legal limbo", Justice William Young said yesterday, adding that he would not be a resident of either country once released and unable to return to New Zealand.

Two other people have been tried and convicted in Egypt and Australia for the people-smuggling operation.

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Justices Young, Ellen France and Mark O'Regan reserved their decision.

Radhi was living in Indonesia at the time of the sinking, having arrived there in March 2000.

He was subsequently recognised as a refugee under religious persecution grounds by the United Nations High Commissioner for Refugees and put forward for inclusion in New Zealand's annual quota intake of refugees.

New Zealand granted Radhi refugee status, and he and his wife and two children arrived in New Zealand in March 2009. Upon arrival, he was granted a residence permit.

However, in October 2010, Australian authorities submitted an extradition request
to New Zealand and in 2011 Radhi was arrested.

Legal proceedings have been ongoing since then as he fights the extradition process.

Radhi's third child was born in New Zealand and his family now lives in Auckland.

- Additional reporting NZN