Labour Minister Simon Bridges ignored advice from Ministry of Business Innovation and Employment to raise the minimum wage to between $13.80 and $13.90 an hour.
The new minimum wage of $13.75 came into effect this week.
In the annual minimum wage review, the ministry advised Mr Bridges that raising the minimum wage to $13.80 was recommended, in line with this year's forecast CPI changes.
Modelling carried out by the ministry and released under the Official Information Act shows the minimum wage could be increased to $13.90 before it would noticeably constrain employment growth.
The option was also in line with the annual increase in the median total hourly earnings, according to New Zealand Income Survey last year.
The ministry's policy manager Cherie Engelbrecht and general manager of labour environment Kirstie Hewlett compiled the report, which showed there are 84,000 people on minimum wage and a further 221,000 low wage workers being paid between $13.50 and $15 an hour.
The report found minimum wage workers are more likely to be female, Maori or Pacific Islander, without formal qualifications, and part-time employees or those working in the retail and hospitality industries.
During the wage review the ministry consulted with Treasury, who recommended retaining the previous minimum wage rate of $13.50 an hour, or raising it to $13.60 an hour.
The Ministry of Social Development and Ministry of Women's Affairs supported an increase to $13.80 an hour.
The Ministry of Pacific Island Affairs called for an increase to $15 an hour, and the Labour Partly said it would increase the minimum wage to $15.
Te Puni Kokiri proposed that the adult minimum wage be raised in steps over four years to $18 an hour; with the first increase to $16 this year, then increases to $16.60 and $17.30 per hour over the ensuing years, subject to favourable economic recovery.
The New Zealand Council of Trade Unions asked for an increase in the minimum wage to $18.44 an hour, with an interim step of increasing the minimum wage to $15 from April 1.
The ministry said increasing the minimum wage to $18.44 would constrain employment growth by 25,000 jobs, increase annual wage costs by $2.6 billion and increase inflation by 1.27 per cent.
The impact of increasing the minimum wage to $15 an hour would increase annual wage costs by $315m and cost the Government $67.87m.
In February a coalition of community groups called for a national living wage of $18.40 an hour.
The figure was based on the cost of Otago University's University's "basic"food diet for a couple with two children ($226 a week), the national lower-quartile rent for a three-bedroom house ($275 a week), and other costs totalling $537 a week based on the average spending by families earning below the median household income for couples with two children.
The ministry has changed the way it carries out its annual minimum wage review. It will carry out a comprehensive review every four years and a streamlined review every other year.