The woman was a dual citizen of Australia and New Zealand, but Australia stripped her citizenship under anti-terrorism laws.
Ardern said the woman had lived in Australia for most of her life and had travelled to Syria on her Australian passport.
We believe Australia has abdicated its responsibilities in relation to this person and I have personally made that point to Prime Minister Morrison," Ardern said in an unusually blunt statement.
It is wrong that New Zealand should shoulder the responsibility for a situation involving a woman who has not lived in New Zealand since she was 6."
But Morrison said he was simply doing his job by protecting Australia's interests.
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, Morrison said. "And I think Australians would agree with that.
Morrison said a 2015 Australian law that automatically cancels the citizenship of dual nationals who engage in terrorism is clearly understood.
Turkey's Defense Ministry said the woman, who was wanted on an Interpol notice for allegedly belonging to the Islamic State group, was caught, along with the children, by border security units while trying to sneak into the town of Reyhanli, in Hatay province.
For the past two years, Turkey has been stepping up efforts to send home foreign fighters, saying the country shouldn't be seen as a hotel for Islamic State militants.
The repatriation push was in retaliation for the refusal by Western nations to back a Turkish incursion against Syrian Kurdish fighters, whom Ankara considers terrorists. Many countries voiced concerns that the incursion into Syria would lead to a resurgence of the Islamic State group.
Turkey has also intensified security along its border with Syria to prevent infiltrations and regularly carries out raids against suspected Islamic State militants.
Ardern said the welfare of the children needed to be considered, a point she'd be raising with both Turkey and Australia.
"These children were born in a conflict zone through no fault of their own," Ardern said. Coming to New Zealand, where they have no immediate family, would not be in their best interests.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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