Local police confirmed the woman was the mother of the two children found with her at the Turkey-Syrian border.
A spokeswoman for the Prime Minister refused to say whether Jacinda Ardern had been briefed on the case, or whether the woman's identity was known to New Zealand authorities.
She said no information would be forthcoming from the Prime Minister until she made her way to Parliament prior to 2pm when press gallery journalists would have the opportunity to quiz her.
Police told Newstalk ZB they had been in contact with the NZ Embassy in Ankara.
They say the woman is likely to face deportation to New Zealand.
New Zealand's Ministry of Foreign Affairs and Trade said it is "aware of the situation".
Overseas media reports say the woman was wanted by Interpol with what is dubbed a blue notice.
A blue notice is an international alert, circulated by Interpol, to locate, identify or obtain information on a person of interest in a criminal investigation.
It differs from a red notice, to seek the location or arrest of a person wanted by a judicial jurisdiction or an international tribunal with a view to his or her extradition.
Intelligence expert Dr Paul Buchanan, of 36th Parallel Assessments, said the blue notice indicated the woman was sought for information rather than acts of terrorism.
"It's a notification they want to get information on a person. It doesn't mean she's been doing anything bad. Walking across the border with kids would seem to indicate she was a camp follower or concubine."
He said that would fit with the role of women in the Islamic State of Iraq and Syria, or Daesh.
During the peak of ISIS in 2014-2015, the would-be Caliphate sought to import male foreign fighters but also women who would produce future generations.
"We have yet to determine if she was a fighter or a breeder," he said, although the religious confines and structure of ISIS suggested the latter. "I seriously doubt she would be a fighter."
Buchanan said it was likely she would fit the description of those who were described at the time as "Jihadi brides" - primarily young women who were indoctrinated online or by local recruiters to travel to ISIS territory where they would marry fighters.
If so, Buchanan said it was also possible the woman was from Australia.
In 2015, the prospect New Zealanders were among those women who had travelled to marry fighters was raised by NZ Security Intelligence Service director-general Rebecca Kitteridge.
She told Parliament's Intelligence and Security Committee that there had been growing numbers of New Zealand women travelling to areas controlled by ISIS.
She told MPs: "Something that has changed over the last year is the issue of New Zealand women travelling to Iraq and Syria, which is something we haven't seen previously or been aware of."
Then-Prime Minister John Key asked Kitteridge if they could be called "jihadi brides".
The exchange caused a furore over the prospect of women travelling from New Zealand to join the would-be Caliphate. It later emerged none of the dozen women known of by the NZSIS left from New Zealand. Instead, they had travelled from Australia.
The claims led to puzzlement from New Zealand's Muslim community, and then demands for an apology with the Islamic Women's Council submission to the Royal Commission of Inquiry into the Attacks on Christchurch Mosques saying it had caused a rise in hostility towards New Zealand's Muslim community.
Buchanan said the primary focus needed to be on the humanitarian rights of the woman and particularly the children she had with her when she crossed the border. When she returned to New Zealand, legislation existed that would allow her involvement with ISIS to be closely examined, and prosecuted if necessary.
He said the children would be New Zealand citizens by maternal right and it was critical the Government took steps to make sure they were safe and were able to be returned to New Zealand.
Buchanan said it was highly likely the NZSIS would want to speak with her, particularly in the hope of receiving intelligence about missing Red Cross nurse Louisa Akavi, a New Zealander who was taken hostage by ISIS in 2013 and has been missing since.
Green MP Golriz Ghahraman said it was important to bring the woman and her children back to New Zealand.
"Right now, the safety, the rights and wellbeing of these children should be paramount. We have a responsibility to bring our people home."
However, she said New Zealand also had a legal responsibility to determine the mother's culpability in any terrorist activities and to prosecute.
"If she has been contributing to terror, the Syrians - the victims of terror - don't have the resources to make themselves safe right now."
If it were the case she returned with behaviours or an ideology that raised our threat level, that also needed to be managed. "Then we have to make New Zealand safe," she said.
Ghahraman, a former United Nations lawyer, said New Zealand's foreign fighters legislation was designed to manage those who repatriated from conflicts such as that which sprawled across the Middle East during the rise of the would-be Caliphate.
She said the age of the woman now - 26 - and the timing of movement of young women to ISIS during its peak suggested she would have been very young when she went there.
