The office of New Zealand's Prime Minister has described a phone call last night with Australia's Scott Morrison as "constructive".
The woman, named by the ABC as Suhayra Aden, was wanted through an Interpol blue notice, according to the Turkish Ministry of National Defence. The ministry alleged the woman was a terrorist with Islamic State.
Last year, Australia stripped the woman of her citizenship, despite having lived there from the age of six and travelled to Syria from there on an Australian passport in 2014 - at the height of Islamic State's power.
Today a spokesperson said, "regardless of the steps taken in this case to date, both NZ and Australia acknowledge that this case now has a number of complexities".
The statement said Australia and New Zealand are "working through those issues in the spirit of our relationship".
Collins says terror suspect case 'should be Australia's problem'
National Party leader Judith Collins told Morning Report it was difficult to say New Zealand had much moral obligation towards the woman when she lived most of her life in Australia.
"She's a problem that really should be Australia's problem and instead we're the ones left holding the issue. Let's wait to see what the Turkish courts do with her, but I feel very sorry for her two little children and imagine what hell they've been through."
On the rift with Australia, she said it was "very difficult" to see the relationship improving in the near future, adding that the situation was not being helped by recent comments from Trade Minister Damien O'Connor on Australia's dealings with China.
"I can understand the frustration that the New Zealand government finds when they're dealing with a country that actually a lot of New Zealanders live in, a lot of New Zealanders look to Australia and have got family there as well, so they're in a difficult position. One of the issues ... is that New Zealand tends to feel it needs Australia more than Australia feels it needs New Zealand.
On the other hand, she said the two countries had a good working relationship and the Australians provided help in matters of national security and defence.
Otago University professor of International Relations Robert Patman told Morning Report the prime minister had raised a problem in public, which may have been kept behind closed doors in the past.
"The prime minister's global profile has increased with her handling of the Christchurch terror atrocity and also her handling of the Covid-19 crisis, so I think she may feel she's now in a position to speak out on a issue which quite frankly does need to be addressed. It's no good tiptoeing around it.
"The Australians in this situation have shown hypocrisy and a lack of strategic realism."
With a lot of countries now facing the same problem, he said this issue was "a two-way loyalty street".
"Many western countries have seen their citizens participate in the Syrian civil war, often on the side of Islamic State. And a lot of them are disowning them and that's completely irresponsible.
"I was personally unhappy about the way New Zealand handled the case of Mark Taylor.
"In a sense, we don't want Australia to offload their problems on us but we mustn't export our problems elsewhere either. In other words, I think all countries - including western countries - must take these citizens back, they must bring them to justice, they must take them out of circulation and they must prevent the possibility they'll be free to continue causing mayhem on the international stage."
'I feel very disappointed for New Zealand' - Collins
Judith Collins said there needed to be discussions about how New Zealand would deal with these cases, "because there's likely to be a few more like this".
"I think it's something we need to start having a conversation... I feel very disappointed for New Zealand that we've ended up with this [situation].
"I think it's something New Zealand does need to start inquiring why it is that Australia can take action while New Zealand is left screaming about it ... but ultimately at the receiving end of it.
"I think it's one of those things where it's best if we can have a multi-party agreement on how to handle a situation of national security that we need to take extremely seriously."
In 2019, the Terrorism Suppression Bill, which gives the government more powers to impose restrictions on people who have been involved in terrorist activity overseas, became law.
Asked whether it would be right to revoke citizenship of people in these cases, she said: "I think what is right is that New Zealand continues to put the best interests of our country first when it comes to how we deal with international terrorists. Our country has been blessed in many ways, but we've seen what's happened when we've had a terrorist on our shores, and 50 people died as a result of it, we don't want to see terrorists of any sort here."
Collins said the government previously made their stance quite clear, with the case of Mark Taylor. The Kiwi was a self-claimed ISIS member who fled the group and was detained by Kurdish forces, but the government decided not to reissue a passport for him nor facilitate his return despite his pleas.
"I'm not sure that this woman is in a much better situation, but I do feel the children need to be looked after and ... presumably they will have extended family who could assist with them."
Australia has 'moral responsibility' - Anjum Rahman
Islamic Women's Council of New Zealand spokesperson Anjum Rahman told Morning Report that even if the woman was convicted, it's unlikely she would have been radicalised when she left New Zealand at the age of six.
"However her thinking was shaped, it happened in Australia. Her family is in Australia. We know that any successful rehabilitation and deradicalisation works better if there's family support."
She said those who do leave to ISIS areas after becoming radicalised were often young people who are impressionable.
"We do need to wait and see what the process is through the justice system in Turkey and what evidence they present and whether she's convicted.
"But regardless of all that, the fact she went to Syria at that time means that her thinking was probably not of the best and that needs to be dealt with," she said, adding that rehabilitation would be in the best interests of the children.
ABC also reported she had another child who died of pneumonia while in Syria. Rahman said various tough experiences would also mean there needed to be a plan in place to support her.
"I understand the police are working deradicalisation programme, they've been funded to do that. That will need to be escalated to ensure that she's not left on her own because that will be a bad outcome for those children, they need the best support they can get and that support will come from the mother."
However, Rahman said it would have been preferable for the mother and children to return to Australia. She said Australia has a big problem with radicalisation, with reference to past cases of Mark Taylor and the Christchurch mosque shooter. In 2019, ABC reported Taylor had lived in Australia on and off for 25 years.
"They need to get their house in order. I don't know if there's any legal recourse or anyway they can be forced to take this woman but they have moral responsibility and one would think the international community would put pressure on Australia to take care of someone who spent a major part of their life in that country."
She said if the woman was left in Turkey then she probably wouldn't get any support, leaving the children in a precarious situation.