New Zealand's Prime Minister Jacinda Ardern has accused Australia of "abdicating its responsibilities" amid a row over a woman accused of having links to the Islamic State (IS).

The woman is facing deportation to New Zealand after being caught entering Turkey from Syria with two children.

But Ms Ardern says the dual national should be sent to Australia.

The 26-year-old held both Australian and New Zealand citizenship until Canberra revoked it last year.

However, Ms Ardern pointed out that the woman - who the Turkish Ministry of National Defence has identified as a member of IS - had not lived in New Zealand since she was a child.

"They left New Zealand at the age of six, were resident in Australia from that time, became an Australian citizen, left from Australia to Syria, and travelled on an Australian passport," she said.

She summed up by saying: "New Zealand frankly, is tired of having Australia exporting its problems."

Mr Morrison responded by saying his job was to protect "Australia's interests".

He added that legislation passed in parliament automatically cancels the citizenship of a dual citizen accused of being engaged in terrorist activities.

Mr Morrison said he was scheduled to speak with Ms Ardern today.

This is not the first time a citizenship row has erupted over a terror suspect.

In 2019, Shamima Begum - the schoolgirl who fled London to join the Islamic State - was stripped of her UK citizenship.

Ms Begum is believed to be eligible for Bangladeshi citizenship through her mother. But Bangladesh's ministry of foreign affairs refuted this, adding that there was "no question" of her being allowed into the country.

Ms Begum has launched an appeal to have her citizenship restored.