The Foreign Minister has received an assurance from his Australian counterpart that the death of a New Zealander in an Australian prison is now the subject of a full inquiry.
Murray McCully met with Julie Bishop in New York to discuss the case of Junior Togatuki, and the broader issue of some New Zealanders with criminal records being detained and potentially deported.
New Zealand-born Togatuki, 23, moved to Australia with his family when he was four years old.
Although his prison sentence ended in August, he was kept in a high-security New South Wales prison awaiting deportation after his visa was revoked. He died in the prison two weeks ago, with authorities saying he committed suicide.
His sister, Jean Togatuki, said he had no memory of New Zealand. He had written to Australia's immigration minister Peter Dutton begging to be allowed to stay in Australia.
Ms Bishop said a full inquiry was being made into the case.
Mr McCully also told Ms Bishop Prime Minister John Key wanted to discuss the issue with Australian Prime Minister Malcolm Turnbull.
The news comes after Labour leader Andrew Little criticised the way the Foreign Affairs Minister had responded to Australia's treatment of some New Zealanders, since migration laws were changed.
Mr Little told Morning Report Australia's policy was "brutal" and he dismissed Foreign Affairs Minister Murray McCully's response as inadequate.
Mr Key told reporters in New York earlier this week that Mr McCully had texted Australian Foreign Minister Julie Bishop about the issue.
Mr Little said, "Sending a text message doesn't cut it."
Proper diplomatic action was required, he said, and the government should have instructed the New Zealand High Commissioner in Canberra to make recommendations to the Australian government.
The Australian government has been cancelling New Zealanders' visas at the rate of 10 a week since it toughened up the Migration Act last December.
Mr Little said that Australia and New Zealand claimed to be kindred spirits and were close allies, and needed to manage their relationship maturely.
"We should be saying to them that some of the people that are being detained are people who left New Zealand in their infancy. It would be inhumane for them to be deported to New Zealand, simply on the grounds that they were born in New Zealand," he said.
"I'm calling for the policy to be applied in a realistic and humane way."
He hoped for better, more effective dialogue with Australia in the future to resolve problems with the policy.
Queensland senator Ian Macdonald said that New Zealanders who had been in Australia since infancy or childhood should apply for citizenship if they felt Australia was their home.
But Mr Little said this was not a realistic option for many.
"I suspect there will be a lot of Kiwis in Australia [that don't think about] whether to apply to citizenship until well into their adult lives, but they shouldn't be treated like a New Zealander with roots and a home in New Zealand that they can easily be planted back into."
'Thumbing its nose'
Meanwhile, the head of a human rights law centre across the Tasman said the Australian Government was thumbing its nose at its international obligations after impeding a visit to its detention centres by the United Nations.
About 200 New Zealanders pending deportation are estimated to be among those being held at the centres, including a facility on Christmas Island.
The UN Special Rapporteur on Human Rights of Migrants cancelled a visit this week when Australia refused to guarantee detention centre staff could talk to him without fear of legal reprisals.
Human Rights Law Centre executive director Hugh de Kretser told Morning Report the secrecy was damaging Australia's international standing.
"If we want to achieve democracy, human rights - the things that matter to us, that enable us to have security and prosperity - we need a good reputation, internationally. We need to be promoting good standards.
"We need to promoting human rights, not undermining human rights," he said.
He said there were repeated reports of abuse at the centres.
Thousands of New Zealanders may be deported
The Australian Lawyers Alliance said the number of New Zealanders being kicked out of Australia because of criminal convictions could eventually run into the thousands.
About 300 people have been deported to New Zealand or are being detained while a decision is made on their visa, since tough new laws came into force in Australia last year.
Australian Lawyers Alliance National President Greg Barns said New Zealand was the hardest hit of any country under the new policy.
He said immigration officials were rounding up many of the 5,000 New Zealanders who had served more than 12 months in jail, including many who served their time a long time ago.
1,500 others are currently in Australian prisons.
Mr Barns said those being deported had no right of appeal.