Australian Foreign Minister Julie Bishop has met New Zealand counterpart Murray McCully and Prime Minister John Key in New York and afterwards said the Australian Government would talk further about its policy of detaining and deporting non-Australian offenders who have served a prison sentence of a year or more.
Ms Bishop said she would ask Australia's Immigration Minister Peter Dutton to speak with New Zealand Immigration Minister Michael Woodhouse but gave no indication the policy would be reviewed.
She said the New South Wales Police would investigate the death of Junior Togatuki, 23.
Togatuki, who had mental health illnesses, died in solitary confinement in Goulburn's Supermax prison. He had finished his sentence but was being held awaiting deportation to New Zealand, a country he left aged four.
Mr McCully had initially sent a text Ms Bishop about the case, before meeting her in person.
"This week there has been the saga of the New Zealanders being held in Australian detention camps prior to deportation here," Mr Dunne wrote.
"Our response has been to send a text to the Australians about what is going on. I am not standing up for Australian criminals?but the treatment being meted out to them is excessive and out of line with the vaunted special relationship between our two countries."
Mr Dunne pointed to the "appallingly tardy" response to the Syrian refugee crisis and the case of a New Zealander jailed in Myanmar for insulting Buddha as examples of New Zealand being hesitant to become involved until public opinion demanded it.
His stinging criticism comes as Greens parties in Australia and New Zealand jointly call on the Australian Government to stop the indiscriminate deportation of New Zealand offenders from Australia.
"Every case is different and should be considered individually, " Australian Greens' immigration spokeswoman Senator Sarah Hanson-Young said.
"With multiple suicides and suicide attempts in recent weeks, it's clear the situation is untenable and an emergency network-wide audit of support services in required."
Deputy Prime Minister Bill English said he did not accept Mr Dunne's criticisms.
Talking on Newstalk ZB to Larry Williams drive-time, he said the Government pursued considered and focused interventions when it needed to.
On the claim that the Government was slow to act around the issue of the Syrian refugees, he said: "There was no reason at all why a sensible Government wouldn't take a few days to consider the scale and nature of New Zealand's intervention."
Asked about the Government's relationship with Mr Dunne, he said it revolved fundamentally around what he willing to vote for.
"We always find him approachable and reasonable and on some issues, selectively, he is very testing and pretty demanding and that is what you would expect of a coalition partner.
"It is a strong functional relationship but it's one where there is probably a bit more to-ing and fro-ing in it than people might realise."
New Zealand Greens human rights spokeswoman Catherine Delahunty said that New Zealand made humanitarian exceptions on case by case basis for people who were in extraordinary circumstances.
Mr Key intends to discuss the issue of deportations with Australia's Prime Minister Malcolm Turnbull, who took over from Tony Abbott just over two weeks ago.
About 200 New Zealanders are being held in seven detention centres awaiting deportation.
