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 has been known to New Zealand and Australian authorities "for some time", Ardern said.

The woman 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.

New Zealand authorities raised concerns with their Australian counterparts that in the event of her detention or return about which country should be responsible.

Ardern 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 uni-laterally 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 Governmentt 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 gage as an enemy of our country."

Earlier, Ardern said she was most concerned for the two small children the woman 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 says the 26-year-old 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 woman's citizenship sits with New Zealand currently but Ardern said she would continue to raise the issue with Australia.

Ardern warned Morrison when he told her Australia had revoked the woman'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 and then later that year she was informed Australia had revoked the woman's citizenship. It has continuously been raised "ever since".