A payroll blunder that left thousands of state sector workers underpaid may be widespread, meaning many in the public sector and in private businesses may have been short-changed.

The problem came to light after police and more recently staff at the Ministry of Business, Innovation and Employment (MBIE) were underpaid because of an error calculating their holiday pay and shift entitlements.

But Finance Minister Bill English on Tuesday signalled that the problems go back to the Holidays Act in 2004 and "there may be a widespread issue in the public sector as well as the private sector".

Prime Minister John Key said the State Services Commission was investigating whether the problem was broader, although he did not know what was driving the mistakes.

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​If it had happened in two agencies then there was something in the law that made it "tricky" to administer and the Government needed to look at what that was and its effects, Key said.

"Clearly the law hasn't been administered in the way that the law states - why that is, I don't know."

He understood the amounts in each case were small but over a long time and a large number of people they added up.

But State Services Minister Paula Bennett said "other agencies weren't majorly affected" by the problem.

However, she would not say who had provided the payroll system at MBIE.

"I am not prepared to name or blame any company or agency for this issue," she said.

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"The private sector initially alerted us to the problem in 2014, and we have been working through this since then. We've spent the last year looking across Government, and to date Police and MBIE are the only State-sector agencies reporting significant issues, and it took them months to figure out the extent of the problem owing to the complexities of accounting for so many different individual pay rates."

MBIE Minister Steven Joyce has said the underpayments could total in the millions of dollars and affect up to 3000 people.

Police have already paid out more than $30m to staff to correct their underpayments, but no figure has been put on MBIE's bill.

English said some private companies had raised with him whether they may also have been miscalculating the Holidays Act requirements.

He said Police had found the money from within their funding and it was assumed MBIE would too. People must be paid what they are entitled to.

English said he did not believe it was an issue of "lack of competence" but was due to the complexity of the Holidays Act. The "sheer complexity" of that law meant there was a higher likelihood software writers got it wrong.

But at this stage the Government did not know how big the problem was.

However Labour leader Andrew Little, a former union boss, said the blame should be sheeted home to the Government and those running the agencies.

"If anybody came to me and said 12 or more years after the implementation of a piece of legislation 'we've got these problems and it's the fault of the legislation' I would laugh at them - probably out of court ... The fact that it's taken 12 years to get to this point and one of the largest government departments - the one responsible for administering the Holiday Act - now discovers there's a problem; it beggars belief."

Joyce said the system containing the errors was installed more than 10 years ago at the Department of Labour but was used for the merged super-ministry MBIE in 2012.

"It's disappointing, but around an area that's fiendishly difficult, and that's not to excuse it," Joyce said.

The providers of the system were working to fix the problem as quickly as they could, though that could be "weeks to months away".

MBIE chief executive David Smol told TV3 there had been isolated issues with the payroll systems some time ago, but a more systematic review in 2014 and system "health check" in 2015 revealed the problems were more widespread than initially thought.

"We've had specific issues with people coming forward and saying, 'My pay doesn't look right', that's typical of payroll systems.

"That's prompted us to do a more thorough investigation, in conversation with the labour inspectorate, [that] revealed a wider range of issues than first thought."

​Smol said it was unclear how much the payroll errors could cost taxpayers, but MBIE wanted to solve the problems as soon as possible.

"We shouldn't be in this situation, it's not fair on our people - we are very committed to putting it right as quickly as we can and making sure we've got good arrangements for the future."