WELLINGTON:New Zealand's Prime Minister Jacinda Ardern on Tuesday accused Australia of abdicating its responsibilities by "unilaterally" cancelling the citizenship of a woman detained in Turkey with alleged links to the Islamic State.

Turkish authorities said on Monday that three New Zealanders, including a woman alleged to be a member of Islamic State, have been caught trying to enter Turkey illegally from Syria.

The woman had held New Zealand and Australian citizenships, but the Australian government unilaterally cancelled her citizenship, Ardern said in her statement.

Ardern said it was 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, has resided in Australia since that time, has her family in Australia and left for Syria from Australia on her Australian passport.

"Any fair minded person would consider this person an Australian, and that is my view too," Ardern said.

"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 referring to Australia's leader.

Turkish authorities said the 26-year-old woman was identified as a DAESH (Islamic State) terrorist. Ardern said she had been travelling with two children.

"The welfare of the children also needs to be at the forefront in this situation. These children were born in a conflict zone through no fault of their own," Ardern said.

"We will be engaging with the Turkish authorities, and given there are children involved, their welfare will be top of mind in our response,” she said.