Prime Minister Jacinda Ardern says the New Zealand woman identified as an international terrorist by Turkish authorities should have been deported to Australia.
The woman, named by ABC as Suhayra Aden, has been known to New Zealand and Australian authorities "for some time", Ardern said.
The 26-year-old left New Zealand at 6-years-old to live in Australia and became a citizen. She left from Australia for Syria and travelled on an Australian passport.
It is a series of events that has also brought frustration from our Muslim community, with Islamic Women's Council national co-ordinator Aliya Danzeisen saying: "Australia just keeps sending people back to us. It smacks of injustice and a lack of partnership."
Ardern said New Zealand authorities had raised concerns with their Australian counterparts that in the event of her detention or return about which country should be responsible.
She said she raised the issue directly with Scott Morrison and ask that they work together.
"I was then informed in the following year that Australia has unilaterally revoked the citizenship of the individual involved. You can imagine my response," Ardern said.
"This is clearly an individual whose links sit most closely with Australia."
Morrison then told Australian media that he had a call scheduled with Ardern about the woman's case - but he defended Australia's actions.
"My job is Australia's interests. And it's my job as Australia's prime minister to put Australia's national security interests first."
Australian law stipulated that anyone with dual citizenship who "engaged with terrorist activities" had their Australian citizenship cancelled.
"That happens automatically and that has been a known part of Australia's law for some time.
"I understand the New Zealand Government has some issues with that. And I understand that and the Prime Minister and I are scheduled to speak later today. 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 the many others that we'll have.
"Australia's interest here is that we do not want to see terrorists, who've fought with terrorist organisations, enjoying privileges of citizenship that I think they forfeit the second they engage as an enemy of our country."
Ardern: 'NZ tired of having Australia export its problems'
Earlier, Ardern said she was most concerned for the two small children Aden was detained with.
"I think New Zealand, frankly, is tired of having Australia export its problems. But now there are two children involved so we have to resolve this issue with those two children in mind."
The Republic of Turkey's Ministry of National Defence said the woman is an Islamic State terrorist.
"Three New Zealand nationals including an adult and two children were caught by our border guards in Hatay's Reyhanlı district while trying to enter illegally from Syria," a ministry statement said.
"The adult, a 26-year-old woman named S.A. was identified as a Daesh [Isis] terrorist wanted with a 'blue notice'. The captured terrorist was handed over to the Reyhanli Public Prosecution Office."
Ardern said New Zealand has obligations with its citizens to bring them back in these scenarios regardless of whether they have committed offences - especially when there were two very small children involved "who did not choose to be born into a war zone".
Legally the Aden's citizenship sits with New Zealand but Ardern said she would continue to raise the issue with Australia.
Ardern warned Morrison when he told her Australia had revokedAden's passport that she would "speak very strongly on New Zealand's view" publicly.
"He has been forewarned of that continuously. So this morning I did the same. I reminded him that I would be raising this issue very strongly."
Ardern said she wanted to work through the issues bilaterally with Australia.
"I never think that the right response was to simply have a race to revoke people's citizenships - that is just not the right thing to do.
"We will put our hands up when we need to own a situation - we would expect the same from Australia. They did not act in good faith."
Ardern said they were looking to find a resolution "in a timely way" because children were now involved but couldn't put a timeline on it.
She has asked officials to ensure there is a welfare check on the children.
Ardern called the relationship with Australia "important" in which they shared frank opinions on issues which she valued.
"But I cannot hide the feeling I have, strongly on behalf of New Zealanders, about what's been done here because it's simply not right."
Ardern said she first raised the issue with Morrison early on in her time as Prime Minister. Later that year she was informed Australia had revoked the Aden's citizenship. It has continuously been raised "ever since".
National foreign affairs spokesman Gerry Brownlee said the Australian Government should be engaged with the New Zealand Government on any response to Aden's situation "because it is clearly a dual problem"
"By the same token, I think the New Zealand Government needs to mindful and respectful of the position Australia has taken in order to reach some kind of a solution here.
"The solution in the end may be that nobody does anything."
Asked if he thought Ardern had not been respectful of the Australian Government, he said: "I just think there is a growing number of skirmishes between the Australian and New Zealand Government that we haven't seen in the past."
Islamic Women's Council's Danzeisen linked Australia's action in relation to Aden with its 501 programme that has seen it strip its passports from New Zealand-born criminals and send them back over the Tasman.
"What's on my mind is the concept of country's responsibilities for the people they have helped rear. If Australia was in partnership with New Zealand, they would be assisting with supporting people and addressing these issues of radicalisation."
Danzeisen said the returning gang members was an example that came before Australia's decision to cancel Aden's passport, even though she had lived in the country since age 6.
Danzeisen said the process of radicalisation required strong networks around the individual affected.
"These people who have grown up in Australia have networks and communities they can rely on to build support. Instead, they place them in almost foreign countries. She was a child (when she left New Zealand) and doesn't have the support networks, as far as I know."
If it was left to New Zealand's Islamic community to help Aden, then it would, she said, but believed it would be better with Australia's involvement.
It also raised a question around New Zealand's capability to deradicalise someone such as Aden in Turkish detention, and the financial burden that would fall on the Islamic community to support that, she said.
Danzeisen said she was also concerned the focus on Aden, her purported allegiance with ISIS and her return to New Zealand would lead, again, to heightened adverse pressure on the Islamic community here.
Danzeisen also highlighted the radicalisation of Aden, and the bumbling jihadi Mark Taylor - who spent years in Australia - and the Christchurch mosques' terrorist.
"Australia should look into the radicalisation of individuals."
Islamic Women's Council media spokeswoman Anjun Rahman said there had been recent funding for police to do deradicalisation work, and around establishing a centre of expertise to study the causes of, and ways to prevent, terrorism.
She said the work was important because it wasn't aimed just at cases such as the 26-year-old but others, including those who made threats to mosques.
Rahman said there was also a need to study online algorithms and the way in which it funnelled people into radical thought and behaviour.
It was work the Chief Coroner should undertake as part of the inquiry into the Christchurch shootings, she said.