The changes would eventually give a person an extra $6400 a year, or $125 a week.
The Greens also want a compulsory redundancy payout of four weeks' wages, and to scrap youth wages, 90-day trials for new workers, and The Hobbit laws that make screen workers contractors -- and ineligible for collective bargaining -- by default.
The National Party was quick to dismiss these measures as costing thousands of jobs and putting up more roadblocks for businesses.
The Ministry of Business Innovation and Employment estimates that an immediate increase to a minimum wage of $18 an hour could cost up to 16,250 jobs -- although economic conditions could be different by 2017.
But Mrs Turei dismissed this: "In the US, there are 13 states that have just raised the minimum wage. It's good for the economy, it's good for families. There hasn't been a significant drop in jobs.
"Companies will need to pay more to their workers, and therefore their profits will go down slightly. In return, they get a more stable workforce, better productivity and greater commitment.
"The question is: should families get a fair reward for the work that they do? Right now, they do not."
National's Labour spokesman Simon Bridges youth wages let younger workers get a foot in the door, while a third of employers have said they would not have hired people without the 90-day trial.
The policy, including boosting public sector wages, would cost $1.18 billion over four years, but this would be more than offset by $1.9 billion in extra tax revenue from boosting the minimum wage.
The numbers did not reflect any reduction in company tax revenue from lower business profits.
National's economic development spokesman Steven Joyce said this was "fanciful".
"If they really think it would work, why not knock everyone through to $30 an hour, and then the tax department could really make some money."
Cleaner Charmaine Reihana, who was at the policy launch, said living on the minimum wage of $14.25 and supporting two children was impossible.
She had recently been given a raise to $14.60 an hour.
"We got more bread on the table, more milk in the fridge, but just surviving. It sux.
"It's very hard to try and put money aside for rent, power, forget about a phone. No landline, no internet for the kids.
"And even tougher for my kids, because I'm never home ... My neighbours look after my kids, thank God for them."
Lo Boca Loca restaurant owner Lucas Putnam says paying his staff the living wage has added about $1000 a week to his business costs, but workers are more committed and working harder as a result.
"People before profit," he said.
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