The Prime Minister says Grant Robertson should apologise to the chief statistician for a "below the belt" comment inferring Statistics NZ was politically motivated.
The department on Wednesday released data on a new measurement of underutilisation in the workforce for the first time following a rejig of the Household Labour Force Survey.
It looks at the potential labour supply, which includes people who are working but want more hours, those who want a job but aren't actively looking or available, and those officially defined as unemployed.
There were 342,000 people who fit into that category, or 12.7 percent.
The change meant those just looking at job ads online or in newspapers weren't counted as actively looking for a job.
Labour and income statistics manager Mark Gordon says the measurement will be used as a better way to "understand the untapped potential" in the labour market.
On Tuesday, Mr Robertson, Labour's finance spokesman, accused the Government of "actively massaging" data by changing how the joblessness is measured.
It was something government statistician Liz MacPherson took offence at, saying she and her predecessors were "fiercely protective" of the independence of their role.
"This independence means that I maintain the right to make changes necessary to ensure the relevance and quality of our official statistics. Changes to the Household Labour Force Survey [HLFS] have been made to ensure that we produce the best possible measure of the current state of the labour market and to maintain consistency with international best practice.
"Far from ignoring technological change during the past 30 years, such as the advent of the internet, we are incorporating these changes so as to be technology neutral."
On Wednesday, Mr Robertson maintained the change "doesn't make sense to me whatsoever".
However, Labour has to use the figures the department produces.
"I do question whether those are appropriate changes, but that is her right to make those changes."
The data also showed the unemployment rate was 5.1 percent, though Mr Robertson didn't believe that was correct. He also said the Government had a "track record of misusing statistics".
John Key says Mr Robertson should know "better than anyone else there's no political interference".
"People know we can always disagree about the HLFS or any other stat that Stats NZ might produce, but one thing they're not is politically motivated.
"At the end of the day, I don't think attacking the chief statistician is anything other than a bit below the belt."
Council of Trade Unions economist and policy director Bill Rosenberg is disappointed the unemployment rate is "falling so slowly".
"We're supposedly a booming economy, some people would object to that. Unemployment could be down to the 3.3 percent it was in 2007, but instead it's 5.1 percent and that's 131,000 people officially unemployed."
Mr Key says while the Government would "always want to create more jobs and do so faster", the economy is still "growing pretty strongly".
Employers and Manufacturers Association chief executive Kim Campbell says the figures show a "perfect situation" where unemployment is falling, and vacancies are increasing.
He says the rate at which unemployment is dropping has been mitigated by the record number of migrants.
"And still our unemployment figures are coming down, so it means the economy is absorbing all of these new people very well."
Formerly known as the Household Labour Force Survey (HLFS), the Labour Market Statistics survey was recently re-developed. The June quarter results are the first batch of data from the new method and also include data from the HLFS. The publication was delayed from August 3.
The new figures also show 1000 fewer people were unemployed in the June quarter compared to March, bringing the jobless rate down to 5.1 percent, though Labour has disputed whether this figure is accurate.
Wednesday's Labour Market Statistics release shows unemployment is also down compared to the same time last year - 5.5 percent in the June quarter - particularly among women.
"Compared with June 2015, there were 8000 fewer unemployed women, and their unemployment rate fell from 6.2 percent to 5.4 percent," labour and income statistics manager Mark Gordon says.
In unadjusted terms, Auckland is also experiencing its lowest unemployment rate since the September 2008 quarter - 4.7 percent compared to 4.1 percent respectively.
Meanwhile, the Ministry of Business, Innovation and Employment says the number of online job advertisements is steady - up 0.2 percent between June and July, but up 12.7 percent over the past year.
The survey looks at job vacancies on Seek, Trade Me Jobs and the Education Gazette each month.
The number of jobs available increased in six of the eight industry groups, with the main jump coming in the hospitality and tourism sector, up 3.1 percent. The biggest drop was in construction and engineering, down 1.6 percent.
Vacancies were also up in nine out of 10 regions, led by Bay of Plenty (up 2.7 percent), Waikato (up 2 percent) and Nelson/Tasman/Marlborough/West Coast (up 1.9 percent).