A last-ditch appeal against the deportation of a man who claimed to be the world's first climate change refugee has failed.

Associate Immigration Minister Craig Foss has received a briefing on the case of Ioane Teitiota and his family, and has tonight declined to intervene.

That means he will be deported shortly to Kiribati, with his wife and young New Zealand-born children likely to join him.

Mr Teitiota had claimed to be the world's first climate change refugee, but that was dismissed by the courts, and Labour instead asked Mr Foss to allow him to stay on humanitarian grounds.

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READ MORE: Climate change 'refugee' now a humanitarian case

Earlier today, Prime Minister John Key said there was no question that Mr Teitiota was an over-stayer, and not a refugee.

"I am sure people feel for the guy - they have got their family here, all these kinds of things. But unfortunately he is not unique in that, and we have to be in the most part consistent."

On the issue of climate change, Mr Key dismissed the notion that New Zealand should consider looking at accepting people on the basis that their homeland was threatened by rising sea levels.

"I am certainly not ruling out that a future Prime Minister and a future Government wouldn't take that compassionate view, and I suspect actually that they would. But it would be on genuine grounds that they actually can't live in their country."

Labour MP Phil Twyford, whose electorate includes Mr Teitiota's home in Ranui, this afternoon accepted a petition from a Kiribati-Tuvalu delegation from West Auckland, some with tears in their eyes.

Reverend Sumalie Naisali told media that people in Kiribati and Tuvalu were the "vulnerable of the vulnerables", and would be the first to lose their countries to rising sea levels.

He himself had moved to New Zealand to give his children a better future, and that was what Mr Teitiota had done, and his children were born here and knew no other country.

Reverend Naisali said that sending the family to Kiribati was akin to putting someone on dialysis on a plane, despite knowing there was no medical help where they were going.

"There is no employment opportunities in Kiribati, there is population density in Kiribati, there are no education opportunities for the children."

Mr Twyford said focussing on the issue of whether he was a refugee was disingenuous, as the courts had already decided that was not the case.

Instead, Mr Foss needed to intervene on humanitarian grounds, particularly because the children were New Zealand-born.

Green Party co-leader James Shaw said the case was the "canary in the mine", and there would soon be "a flood of people from the Pacific Islands" because of climate change.

Kiribati's capital, Tarawa, is struggling with rapid population growth.

In South Tarawa about half of Kiribati's 110,000 population live within an area of 13km2, with most living in slum-like conditions.

New Zealand is working with other donors to try and address issues, including by improving access to fresh water, upgrading sanitation facilities, and developing a new subdivision just south of Bairiki Airport.