A Kiribati family who claimed to be the world's first refugees from climate change will have to leave their rented house in West Auckland after the father was detained this week.

Ioane Teitiota, his wife Angua Erika and their three New Zealand-born children all face deportation within a week after their four-year court battle for refugee status was rejected by the Supreme Court in July.

But their lawyer, Dr Michael Kidd, has complained to the United Nations Human Rights Committee, which has the power to issue an interim measure barring the deportation.

Waitakere District Court Judge Belinda Pidwell yesterday refused Dr Kidd's request for bail and issued a warrant committing Mr Teitiota in custody until Monday.

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Terri Thompson, for Immigration New Zealand, told the court that deportation orders had been served on the whole family, including the children, and that they would be deported together "within the next seven days".

Mrs Erika, who came to New Zealand with her husband on temporary work permits in 2007, said the family depended on Mr Teitiota's wages from horticultural work to pay rent.

"For me now, I can't afford to pay the rent, I can't afford to feed my kids," she said. "For me, it's better to give notice for our house and everything because I can't afford to pay everything."

The couple's two older children Yolisa, 7, and Tebukaiti, 5, attend Birdwood School in Ranui but Yolisa was in court yesterday with her mum.

"The oldest one understood when the immigration [officers] arrived on Tuesday. She just wrote a note and said, 'I miss you, dad," Mrs Erika said.

"Last night she told me she didn't want to go to school. She said, 'I want to stay home to wait until the last decision for my dad.'"

Dr Kidd told the court that Mr Teitiota had not been able to shower or change clothes while he was held for 48 hours in the Henderson police cells. Mrs Erika brought a suitcase of clothes for her husband in case he was detained further or deported.

Dr Kidd said Mr Teitiota would be detained until Monday in jail, where at least he would be able to shower.

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Dr Kidd's complaint to the United Nations alleges that the New Zealand and Kiribati Governments have failed to ensure "fresh water supplies and the means of life" for the family.

Sydney University law professor Ben Saul, who has taken previous cases to the UN, said the UN committee could issue an interim measure barring deportation until the complaint was considered fully - a process which might take years.

However the committee's final decisions were not binding on member countries.

University of New South Wales professor Jane McAdam, a world authority on climate change refugees, said that although about 20 people had claimed refugee status because of climate change globally, Mr Teitiota was the first to reach his country's Supreme Court and go to the United Nations.

Climate change case

2007:

Ioane Teitiota and Angua Erika arrive in New Zealand on work visas.

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2010:

Visas expire.

2011:

Mr Teitiota is caught at a traffic stop and applies for refugee status.

2013:

Immigration and Protection Tribunal rules he is not a refugee.

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2014:

High Court and Court of Appeal both refuse leave to appeal.

July 2015:

Supreme Court refuses leave to appeal.

Sept 15:

Mr Teitiota detained in Henderson police cells; complains to United Nations.

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Sept 17:

Bail refused; Mr Teitiota committed to jail.

Sept 21:

District Court will hear final pleas.