New Zealand Prime Minister Jacinda Ardern accused Australia Tuesday of shirking its responsibility for a dual national arrested in Turkey over reported links with the Islamic State extremist group.

In an unusually blunt message to her counterpart Scott Morrison, Ardern said Canberra was "wrong" to expect New Zealand to accept the woman, who she said had strong ties to Australia. "Any fair-minded person would consider this person an Australian and that is my view too," Ardern said in a statement. "We believe Australia has abdicated its responsibilities."

The 26-year-old woman was reportedly arrested with her two children this week by Turkish authorities near the Syrian border and identified as a member of IS, also known as ISIS or ISIL.

Ardern said the woman had been a dual Australian-New Zealand citizen until authorities in Canberra cancelled her passport, making her Wellington's responsibility.

"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 six," she said.

"(The woman) has resided in Australia since that time, has her family in Australia and left for Syria from Australia on her Australian passport."

Morrison defended his government's decision as in "Australia's national security 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," he said during a press conference in Canberra.

But Morrison added that he would speak with Ardern further, saying: "There is still a lot more unknown about this case and where it sits and where it may go to next."

Ardern also urged Australia to consider the welfare of the woman's children.

"These children were born in a conflict zone through no fault of their own," she said.

"Coming to New Zealand, where they have no immediate family, would not be in their best interests. We know that young children thrive best when surrounded by people who love them."

Ardern said New Zealand was also engaging with Turkish authorities over the issue.

New Zealand has previously criticised Australia for deporting people across the Tasman Sea who have tenuous ties to the country.

Since 2014, around 3,000 New Zealanders in Australia have had their visas cancelled "on character grounds" -- which does not always require a criminal conviction.

Ardern has pointed out many of those being deported have lived most of their lives in Australia and described the issue as "corrosive" to the relationship between the neighbouring nations.