The detention and deportation of Kiwis living in Australia has been discussed at foreign minister level.
Julie Bishop met Murray McCully in New York on Tuesday, and the next move will involve the prime ministers of both countries.
Mr McCully told Ms Bishop that John Key wants to raise it with Malcolm Turnbull.
There will also be a "wider discussion" between immigration ministers.
"He raised the tragic case involving a New Zealander who died recently in immigration detention and the wider issue of deportations," a spokesman for Mr McCully said.
"With regard to Junior Togatuki, the Australian foreign minister provided assurances that a full inquiry into his death is under way."
New Zealand-born Togatuki, 23, died two weeks ago in a high-security detention centre awaiting deportation.
He had served his sentence for robbery and assault, and authorities say he took his own life.
Togatuki had lived in Australia since the age of four.
Kiwis living in Australia are being detained and deported under new immigration laws which mean anyone who isn't a citizen and who has served a sentence of 12 months or more can be sent home.
There's increasing concern in New Zealand about the way it's being applied to Kiwis, who are affected more than any other nationality because so many live in Australia.
Greg Barns, president of the Australian Lawyers Alliance, says about 1500 New Zealanders are currently in jail and around 5000 have been imprisoned over the last 10 years.
"Certainly, you're looking at the low thousands in terms of the number of people born in New Zealand, who are not citizens, and under this law could be deported back to New Zealand," he told Radio New Zealand on Tuesday.
Nearly 200 New Zealanders are being held in detention centres facing deportation, and hundreds more have had their visas cancelled.
It's been reported that nearly 100 have already been sent back to New Zealand.
And Australian senator Ian Macdonald says Kiwis can't expect special treatment.
"We don't want people who get into trouble, who have a criminal record, and those who fit into that category will have their visas cancelled and sent back to where they came from," he said.
"We love our cousins across the ditch but they must be subject to the same laws as everyone else."
