Ardern said the vast majority of those who would receive the payment were New Zealand taxpayers who were based in New Zealand.
"But we have also moved quickly and so there will be some who are captured by the system, who aren't part of the criteria that's been designed but who may well receive it."
The payment would be distributed by IRD using an automated system so it was not always possible to work out if people were living in New Zealand and the cost of doing so would outweigh any benefits, she said.
The alternative to having these individuals receive the payment would have been an application based process which would have taken too long and it may not have reached those who were most vulnerable, Ardern said.
"The alternative in creating a perfect system would be in creating a less timely payment and potentially those who need it most not being reached."
The payment was one of the measures the government was using to help New Zealanders deal with the cost of living increases in the aftermath of the Covid economic recovery, she said.
"Yes, we've moved quickly, but so has the economic situation."
The payment was still more limited and more targeted than a broad based tax cut, Ardern said.
A tax cut would also likely contribute to inflation but offering a targeted, time-limited payment would limit the possibility of that according to Treasury, she said.
Ardern could not say how many people who did not qualify for the allowance had received it but said that Inland Revenue (IRD) may have that number.
Ardern said she had asked IRD whether individuals who were overseas could be identified based on the interest they were paying on their student loans.
National calls integrated payment 'a major muck-up'
National Party deputy leader Nicola Willis said it was impossible to know the scale of the problem, but she had a sense it was bigger than just a few thousand dollars.
It was not just ex-pat New Zealanders but also former migrants, she said.
"We've been contacted by a man who left New Zealand in 2014, he's now living in India and he got a letter from the IRD advising him he'd be getting the payment."
National had also been contacted by French-working former visa holders and a man who left in 2019 but is now in the Philippines who had also received letters, she said.
"My sense is this is very widespread, it's a major muck-up, it's like the Government pressed 'send all' - it's certainly not targeted and for ministers to be dismissive of it is I think quite disrespectful," she said.
"What a slap in the face to hardworking Kiwi taxpayers who pay tax only for that to be given to people around the world who haven't been in New Zealand paying tax for many years in some cases."
Willis said the problems have occurred because it was a policy made on the fly and she had a lot of sympathy for IRD which is having to administer it.
"Both the Treasury and the IRD explicitly warned the Government against this approach, they advised them that this was not a good way to go, they said 'some people who are ineligible will end up getting it, it'll be very administratively complex, we don't want to do this' and yet the Government pressed play anyway and now we're seeing the results."
National would favour using tax cuts over a government handout since the only people who would get the money would have earned it in the first place, Willis said.
