The National Party is asking the Auditor-General to investigate the government's cost-of-living payment after it was sent to numerous people who were ineligible.

The first of three $116 instalments was paid yesterday to New Zealand tax residents who earn up to $70,000 and not receiving a main benefit.

However, some New Zealanders and former residents overseas have also reported receiving the payout - despite not living in the country - and the government admits it does not know how many.

Revenue Minister David Parker says about one per cent of the more than 2.1 million people receiving the payment - amounting to about $7.35 million - would not have been eligible, but officials do not have an exact number.

National's deputy leader Nicola Willis told reporters this morning the scale of mis-spending could be enormous and she will be writing to the Auditor-General today to request an investigation.

"We know there are a million New Zealanders living overseas, the question is how many of them have a dormant bank account that the IRD has just thrown some money into. It's not good enough to say 'well we think it's less than 1 percent but we don't know'.

"We've had reports of people who've been living in Dubai - 22 years outside New Zealand - someone on the news last night from Australia who hasn't lived here for six years."

She says the cost could "run into the tens of millions". The investigation she's requesting would look into how widespread the problem was and whether taxpayer funds had been used without proper authority of Parliament, she says.

"This is obviously a significant misuse of taxpayer funding, but it's also potentially an issue at law.

"The general policy statement for the cost of living legislation is explicit that the eligibility criteria for that payment require that people be both present in New Zealand for tax purposes and that they're also living here."

She says the right thing to do if people have been paid in error, is to pay it back.

"I think puts New Zealanders overseas in a really invidious position. They didn't ask for this money to go into their account, and now they're in a situation here according to the law they're required to pay it back and I put to you that many of them may not even know that payment's been made yet."

She says the government has been informed throughout the entire process this would happen, and the Finance, Revenue minister should apologise - alongside the prime minister.

"This is a matter that we think is very serious and we think it's unacceptable that the minister for revenue David Parker has admitted he does not know what the scale of the problem is but has also said he will not be investigating it further.

"It's too difficult to do these payments when you're in a roaring hurry and you're making policy on the fly which is what the case was here. This payment was put together in a real rush, and so no one has had time to iron out the wrinkles, to do the data matching, to ensure it's done properly."

Parker says the government was advised that some people would receive the payment despite not being eligible, before Cabinet decided on it ahead of the Budget

"We understood those risks from the start."

He suggests the scale of the problem is not as large as it is being made out to be.

"We know that the vast majority of people who got PAYE at the end of last year are still in work, so we know that the percentage of people for whom IRD's data is inaccurate is a very small percentage."

He says IRD is doing a good job, and the only alternative would have been to require people to apply for the payment, which would have been costly and would have ensured many people who were eligible missing out.

"So the process that we have chosen was preferable."

Willis says a better alternative is to cut taxes.

"The beauty of that approach would have been that no one would have benefited from taxpayer money unless they first paid that tax in the first place."

-RNZ.