Housing New Zealand would be responsible for building 24,300 of them.
"This is a significant undertaking for the Government, for taxpayers, and for our social housing reforms," Adams said.
"It's the equivalent of three and a half new houses on every street across Auckland."
The first phase of the building programme would cost $2.23 billion, of which $1.1 billion would come from borrowing and the rest from Housing NZ's balance sheet.
The second phase would be funded through sales of houses and land, and through rental returns. Housing NZ would also retain any dividends and proceeds from selling surplus properties.
Because 8300 houses will be demolished to make way for the new developments, the net increase in houses will be around 26,000. This included a net increase of 5000 state houses over 10 years.
Many of the old houses were more than 40 years old or had too many bedrooms, Adams said.
About three-quarters of Housing NZ tenants needed one or two-bedroom homes.
The new properties would be a mix of apartments, houses, and terraced housing.
Speaking to media after the announcement, Adams said the "affordable" homes would be priced at less than $650,000. This was the threshold which allowed buyers to get access to first-home buyer grants.
It was not yet known how many of the 20,600 houses being sold on the open market would be priced at affordable levels.
Adams said it was important not to create "social housing suburbs", saying that new developments needed to be a mix of social, affordable, and market houses.
In announcing the initiative, Adams said house prices in Auckland had "added pressure right through the housing spectrum", from emergency houses to homeowners.
Despite evidence that the market was cooling, house prices and rents were still too high, Adams said.
"For those struggling to rent, or to buy their own home, I appreciate that it can be a very difficult situation.
"Most of all, the pressure in the housing market affects those at the bottom."
Labour leader Andrew Little said the National-led Government was finally admitting there was a housing crisis in New Zealand. But its announcement was belated and not credible, he said.
"Auckland currently has a shortfall of 40,000 houses and growing. This plan won't address the shortfall, let alone build the extra houses needed to keep up with demand."
He highlighted the differences with Labour's policy, which is to build 50,000 homes over a 10-year period, all of them in the affordable range.
Green Party co-leader James Shaw said the policy was "too little, too late".
"It's good National has realised that the Government can actually build houses. Now they need to realise that knocking down 8,300 homes and replacing them with 34,000 homes isn't actually enough."
