Adams - who took over the Social Housing portfolio in December - could not immediately say what share of the 20,600 privately-sold homes would have to meet affordability limits.
A spokesman said at least 20 per cent of the 12,900 homes built by Housing New Zealand for private sale would have to be affordable. If this ratio was applied to the broader programme, it would lead to around 4200 new, affordable homes in the city.
Adams said it was important not to create "social housing suburbs" in Auckland, and she wanted new housing developments to have a mix of social, affordable and market-priced houses.
Housing NZ was unable to release details about the locations of the proposed developments yesterday. But the building programme includes previously-announced, large-scale housing developments in Tamaki, Hobsonville and Northcote, where 5200 houses will be built.
In the Tamaki development, the share of affordable homes would be higher, at around 25 per cent.
The 8300 state houses were being demolished because they were too old, in poor shape, or the wrong size for tenants. Adams said her priority would be on re-housing existing Housing NZ tenants before new tenants were offered homes.
It will be some time before new social housing places are created under the Government's plan.
Housing NZ chief executive Andrew McKenzie said 1700 new state house places would be built in the first four years. At last count, there were 2015 people on the official waiting list for social housing in Auckland, and another 600 waiting for a transfer.
Labour leader Andrew Little said yesterday the Government had "finally acknowledged there is a housing crisis". But he criticised National's policy, saying it was "embarrassing" and not credible for a city which already had a shortfall of 40,000 homes.
Green Party co-leader James Shaw said the Government's building plan was too little, too late.
Labour's building programme is more ambitious, promising 50,000 homes in Auckland over the same period, priced at no more than $600,000 for houses and $500,000 for apartments.
Adams questioned Labour's plan, saying there was not room on Crown land in Auckland to build more than 34,000 new homes. The Government was "maximising the available land we have", she said.
"We know the cost, we know the timeframe, we know the building marketability to do it."
She denied Labour's suggestion she had made an election year U-turn, saying the building programme had been in development for two years.