Mark Taylor, 42, told the Australian Broadcasting Corporation he spent five years with Islamic State but fled in December and surrendered to Kurdish forces because conditions had become unbearable.
"There was no food, no money, basic services were pretty much collapsed," he said from a Kurdish prison.
"I was in a pickle myself and had to make a final decision, which was to leave."
Taylor earned his derogatory nickname in 2015 after sending out a series of pro-IS tweets but forgetting to turn off the geo-tagging function, giving away his location.
He told the ABC the bungle earned him 50 days in an IS prison.
He also burned his New Zealand passport in a propaganda video and urged extremists in Australia and New Zealand to "commence operations".
Prime Minister Ardern ruled out stripping Taylor of his New Zealand citizenship because he is not a dual citizen and so has no alternative.
"We of course follow our obligations in international law regarding ensuring we do not deem anyone stateless," she said.
But she also said New Zealand could offer Taylor no consular assistance because it had no diplomats where he is being held and only knew what had been gleaned from media reports.
"We have no connection with the forces detaining him, so it's difficult for us to provide information," she said, adding that Taylor would likely have to contact New Zealand officials in Turkey if he hoped to eventually return home.
Justice Minister Andrew Little said if that happened, Taylor could probably expect to face charges under anti-terror laws.
"It is very clear what happens when you transgress the provisions of that legislation... there's a range of penalties, including imprisonment," he said.
Ardern said New Zealand was not obliged to give Taylor legal representation if he was charged overseas, nor did it have to pay his way home.
Ardern refused to say how serious a threat Taylor would represent if he went back home but said "contingency planning" had been made to ensure New Zealanders were safe from returning jihadis.
She also declined to comment on details of Taylor's ABC interview, in which he insisted he was not an IS fighter and lamented the fact he had been "too poor" to afford a Yazidi slave while with the extremist group.
"I wouldn't want to be drawn on those comments because I do not want to be seen to jeopardise any potential case in the future," she said.