The Council of Trade Unions and community groups say the cost of living is hitting low-income families hard despite inflation falling to its lowest level in 14 years.
Statistics New Zealand figures released on Tuesday show inflation in the year to June was 0.7%, and is below the Reserve Bank's target band.
Inflation has been below 1% for the past year, but the Council of Trade Unions says rising rents, and higher electricity and rates bills, have reduced the spending power of those on low incomes.
Peter Jeffries is chief executive at the Community of Refuge Trust, which builds low cost housing in Auckland and says strong demand and limited supply has prompted landlords to push up rents.
Mr Jeffries says people paid $250 a week on average for a one-bedroom flat 18 months ago. This has jumped a fifth to $300 a week, which has a dramatic effect on those on low incomes.
Council of Trade Unions economist Bill Rosenberg says it's high time hard-hit families saw significant pay rises, which shouldn't worry the Reserve Bank given inflation is likely to remain low for some time.
That is unlikely to happen, with unemployment at more than 6% and firms' keen to restore profit margins following a patchy economic recovery.
And some economists warn significant wage increases would stoke inflation pressures, and force the Reserve Bank to raise interest rates sooner.
ANZ senior economist Mark Smith says interest rates should remain on hold until March next year at the earliest.
"On inflation grounds alone it is very hard it's very hard to make a case for the OCR going up. In terms of other parts of the wider economy in general there could be a case there as the economy strengthens."
Mr Smith says once the pick-up in the housing market has been restrained, interest rates could be brought into play.