Prime Minister Jacinda Ardern says the Kiwi who pledged his loyalty to Isis is "our problem, we have to accept that".
But she this morning confirmed that New Zealand would be making no efforts to get Mark Taylor out of the Syrian prison he is being held in.
Taylor, a former New Zealand soldier who has New Zealand citizenship only, has surrendered to Kurdish forces because life under Isis had become unbearable.
According to ABC, he is being held in a Syrian prison.
Ardern spoke at length about the situation at her post-Cabinet press conference yesterday and this morning reiterated that the Government could not strip Taylor of his citizenship as that would render him stateless.
"If someone came to New Zealand, and was not a New Zealand citizen, and engaged in a terrorist act we would take a very dim view of any country [which] then removed his citizenship and made that person our problem," she told Newstalk ZB.
"He is our problem, we have to accept that."
In other instances around the world where a country has stripped a terrorist of their citizenship, that individual has had dual citizenship.
Taylor only has New Zealand citizenship – revoking that would make him stateless, Ardern said.
"We might not like this problem, but he is still our problem."
Taylor would have to make his way to a New Zealand consulate office to obtain a travel document, and the nearest one is in Turkey.
Ardern said right now, Taylor was in a Syrian prison and the Government "was making no efforts to change that," she told The AM Show.
"However, if he were to find his way to Turkey and seek a temporary travel document, New Zealand cannot make him someone else's problem."
Asked if taxpayers' money would be used to fly Taylor back to New Zealand if he made his way to Turkey, Ardern said: "I am not suggesting that for a moment."
Asked if she had a personal view about if Taylor should return home, Ardern said: "people will probably pick a lot up in my tone".
But she said she didn't want to jeopardise any future investigation New Zealand officials may carry out into Taylor.