Mr Key says the issue has challenged the Anzac bond between the two countries.
New Zealander Angela Russell has been counting the days until she can be reunited with her children after serving three months of a nine-month sentence for theft in two Australian detention centres.*
Having lived in Australia for 37 years and raising a four-year-old son and 17-year-old daughter, the 40-year-old Ms Russell had been looking forward to getting her life back on track.
But all that changed when she received a letter saying she would be among a group of foreign citizens living in Australia who would be deported after serving her jail term.
"It was crazy. I was in tears. I've got two children. I have never heard of anyone, especially in Australia, that can separate mother and children. Like, I would understand if I was in the community and my children were taken off me by welfare, like I had never had any connection with my children. (But) I'm the primary caregiver of (my daughter) Brianna, and we have shared (custody) of my son."
Ms Russell is one of 184 New Zealanders being held in Australian detention centres who face deportation under changes made to Australia's Migration Act last November.
Australia can now deport foreign citizens who have been living in Australia if they have served a jail term of 12 months or more.
The law acts retrospectively to include older offences to meet the 12-month threshold.
Media reports from New Zealand say 119 people have reportedly been deported to New Zealand from Australia so far this year.
That is more than four times the number over the same period 12 months earlier.
New Zealand Prime Mnister John Key told Radio New Zealand the issue is straining the relationship between the two countries.
"There is a special relationship between New Zealand and Australia, and you challenge that relationship to a degree. For people who have committed serious enough offences to mean they have got a jail term of 12 months or more ... but these are also people who have also spent their entire lives in Australia over the years, when they were very young. And it's a little bit like Australians saying, 'We're going to pick and choose. We're going to keep the ones we like, but we're going to send back the ones we don't like.' Well, to a certain degree, I think you have to take the rough with the smooth."
The policy has gained widespread attention after the death of New Zealander Junior Togatuki last month.
The 23-year-old had spent all but the first four years of his life in Australia.
He took his own life at Goulburn's Supermax Prison, where he had been serving a sentence for armed robbery.
The case prompted the New Zealand Prime Minister to have what he calls a blunt conversation with Australian Foreign Minister Julie Bishop.
Mr Key says the issue will be a key focus when he has his first meeting with Malcolm Turnbull.
"There is an Anzac bond and an Anzac spirit, and that means ... I don't know, there is a special relationship that surely means we might get treatment that is different to other countries. And what they might do with other countries is up to them, but I think, when it comes to New Zealanders, the threshold is currently set in the wrong place."
Joanne Cox is from the advocacy group Oz Kiwi, campaigning for the improved treatment of New Zealanders living in Australia.
She says the group has a number of concerns about how the policy is being implemented.
"Our concern is around the double-jeopardy aspect, where the prisoners have served their time and, instead of being released, they are now being deported. And they're quite often toldÿ within the last days of their sentence that they're not being releaased into the community but instead being sent to a detention centre. Once they're on Christmas Island, they have no support system. Their families can't access them, and they don't have access to their lawyers."
Ms Cox says a number of New Zealanders in Australian detention centres are unclear about their fate.
"Several of the lawyers of New Zealanders are speaking out to say they are not being given information on their client and are finding it difficult to even speak to their client, so how can they even take a case or appeal a decision?"
Julie Bishop says she will re-examine the policy.
But she adds Malcolm Turnbull will need to be involved in any further discussions.
Anyone seeking support and information about suicide prevention can contact Lifeline's 24-hour counselling service on 13 11 14.