The Maori Party will continue to push for the minimum wage to rise to $15 an hour, following the decision by the Government on Monday to raise the wage to $12.50.
The Government moved to boost the minimum wage from $12 to $12.50 an hour, in line with the Consumer Price Index.
The new minimum wage rate will come into effect on 1 April.
The training and new entrants' minimum wages will increase from $9.60 to $10.
Maori Party co-leader Tariana Turia said $12.50 an hour is not going to provide any economic opportunity for those on the lowest incomes.
The party will continue to push for a $15 an hour rate which Ms Turia hopes to see in place by the end of the current term of Government.
The Green Party says lifting the minimum wage by only 50 cents an hour is a lost opportunity for the Government to do something far bolder.
Green Party MP Sue Bradford said in a time of recession the country needs lower-paid workers to be earning more, as it is low income earners who stimulate the economy by spending locally on housing, clothing and food.
The Labour Party had called for the minimum wage to go up to $13 an hour, saying putting money into the New Zealand economy at this level would help to stimulate spending.
However, the Government says the latest increase in the minimum wage has hit the right balance between supporting those on the lowest incomes and the cost implications for employers.
Prime Minister John Key said on Monday the Government had to keep in mind the burden on employers if the minimum wage was increased by too much.
Mr Key said it was also important that those earning the least are given some relief in the current economic climate.
Labour Minister Kate Wilkinson said it is clear that, given the recession, a balance was needed between protecting jobs and fair pay for workers.
She said she thinks the right balance has been struck - but for some businesses it would be too much, yet for others it would not be enough.
Ms Wilkinson says there had been wide consultation over the minimum wage, but she refused to say whether Maori Party ministers had been involved in discussions.
Business New Zealand chief executive Phil O'Reilly says the increase is not as large as businesses had feared but is still likely to cost jobs at the margins. He says employers would look first at laying off those with low skills or no skills.
Fast-food company McDonalds said the minimum wage increase will push up its labour costs by $4 million a year.
McDonalds pays the minimum wage to between a half and two-thirds of its workforce.
Managing director Mark Hawthorne said the minimum wage rise will come at a cost for customers.
The National Distribution Union said boosting the minimum wage is not an effective response to the recession and merely maintains the purchasing power of workers.