But the biggest measure is still to come - a Government directive to the councils to scrap their planning limits which determine where and how high houses can be built.
"There will be no room for debate," Mr Key said. "This policy statement will demand that.
"And both for residential and industrial land I think you'll see a further supply on top of all of the other provisions we've made in the Budget."
Auckland councillors voted against densification earlier this year, and will make a final decision on planning limits in August.
Mr Key said the national policy statement will be released "in the next week or two".
"It will have quite firm expectations of matching the supply of land with the expected growth in their community," he said.
"On that basis, you'll see higher expectations on a council like Auckland."
The Government blames Auckland's urban growth limits for constrained land supply, which has contributed to huge house prices rises.
The council rejects this, saying it has approved up to 23,000 homes outside the urban boundaries.
Earlier, the housing initiatives in the Budget were firmly targeted at pressure points in Auckland.
The headline announcements in Budget 2016 - $258 million in social housing and $100 million for surplus Crown land purchases - are designed to ramp up supply in the city and offer support to families with desperate housing needs.
Social Housing Minister Paula Bennett said $200 million would be spent on creating 750 more housing places for people on the social housing waiting list.
"A large portion of this funding is directed at social housing in Auckland, where the tight property market also has an effect on those in social housing."
The surplus Crown land scheme was announced in last year's Budget.
Funding of $52 million has so far secured 13 hectares of land in Auckland, which has potential for nearly 1000 houses, apartments and townhouses.
That funding has now been doubled, meaning it could potentially produce up to 2000 new houses in Auckland.
"The programme's goal is to increase the pace of housing development and to put a greater focus on bringing more affordable housing to the market," Housing Minister Nick Smith said.
The Government also confirmed that a national policy statement would be released soon on urban development, which would direct councils to adjust their plans to allow for more densification. The Government has indicated that if Auckland Council does not agree to adjust its plans, it may intervene.
There are no specific measures in the Budget for first-home buyers, which the Government says are already being looked after through Kiwisaver subsidies.
A $41 million investment in emergency housing was announced ahead of the Budget.
The Government has since confirmed that grants to help house homeless people will be brought forward from September to June.
