In her speech Turei said she would pay the money back if investigated by the Ministry of Social Development.
Turei said she told the story to make a point about how hard it was to survive on a benefit, adding it "made me poor and it made me lie".
In the same speech she launched a Green policy that would increase benefits by 20 per cent and wipe penalties for beneficiaries who fail drug tests or are not seeking work.
Writing in the Guardian Turei said she had since heard from "scores" of people - mainly single mums - who had done the same thing.
"I've also heard from people who are outraged. They think I'm a fraud and a criminal. (Of course, as I've said, I will pay back what I owe.)
"But importantly, all the abuse and vitriol that beneficiaries face today, by the agencies and in private, is now being levelled at me, in public. That reaction was expected. And it has broken the silence about how awful life on a benefit really is."
She said it didn't matter if people changed how they felt about her.
"What matters is what comes out of these conversations, and whether we will see the day when our welfare system is restored to its original purpose - to be a true safety net that helps our people when they need it."
In her speech on the weekend, Turei referenced the case of a woman who killed herself after being wrongly accused of fraud and chased by WINZ for a debt.
In the Guardian article she expanded on that, saying reading about that case spurred her to tell her story.
"Some people have asked why it took me 15 years as an MP to do it. To that, all I can say is that nobody wants to be defined by a lie - I certainly never wanted to be," Turei wrote. "But the outrage and the urgency I felt after reading that woman's story was unlike anything I'd ever experienced. For me, it felt like it was now or never."