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.