Jacinda Ardern has criticised Scott Morrison for what she sees as the shirking of responsibility to a citizen who left Australia to allegedly align with IS.
The New Zealand prime minister spoke on Tuesday of her frustrations with her Australian counterpart, saying "New Zealand frankly is tired of having Australia export its problems".
It comes after a woman and two children were reportedly picked up by Turkish officials for illegally entering that country from Syria. Turkey claims the woman is an IS terrorist with New Zealand citizenship.
Ms Ardern said the woman was a dual Australian and New Zealand national until Australia revoked her citizenship last year.
Ms Ardern said Australia "did not act in good faith" in cancelling the citizenship.
"They left New Zealand at the age of six, were resident in Australia from that time, became an Australian citizen, left from Australia to Syria, and travelled on an Australian passport," Ms Ardern said in Wellington.
"Our very strong view on behalf of New Zealand and New Zealanders, was that this individual was clearly most appropriately dealt with by Australia.
"I raised that issue directly with Prime Minister Morrison and asked that we work together on resolving the issue.
"I was then informed in the following year that Australia had unilaterally revoked the citizenship of the individual.
"You can imagine my response."
Mr Morrison, speaking at a press conference in Canberra an hour later, said it was his job as the Australian prime minister to "put Australia's national security interests first".
"Australia's interest here is that we do not want to see terrorists who fought with terrorism organisations enjoying privileges of citizenship, which I think they forfeit the second they engage as an enemy of our country. And I think Australians would agree with that," he said.
"The legislation that was passed through our parliament automatically cancels the citizenship of a dual citizen where they've been engaged in terrorist activities of this nature. And that happens automatically. And that has been a known part of Australia's law for some time.
"Now, I understand that the New Zealand Government has some issues with that."
Mr Morrison added he was due to speak with Ms Ardern later on Tuesday.
"We speak quite frequently. This is an issue we've discussed before. So I'll leave how we practically deal with those issues to our discussion later today and I'm sure that the many others that we'll have," he said.
"There is still a lot more unknown about this case and where it sits and where it may go to next."
The trans-Tasman relationship has also been strained by , even if they hold no established links to the country.
New Zealanders believe that practice contributes to crime at home.
Moreso, it shows strain at a personal level between Ms Ardern and Mr Morrison.
Ms Ardern said she told Mr Morrison directly that should the woman require public support from New Zealand, she wouldn't attempt to be diplomatic.
"We have continually raised with Australia our view that the decision was wrong," she said.
"My concern however ... is that we have a situation where someone is now detained with two small children.
"If the shoe were on the other foot, we would take responsibility. That would be the right thing to do. And I ask of Australia that they do the same."
With additional reporting by SBS News.
