The Government is working with local authorities to free up more land for housing and to increase supply through fast-tracked Special Housing Areas.
However, councils want more support to build the infrastructure which these developments require, such as roads, water and sewerage.
Mr Key would not be drawn on whether the Budget would include funding for infrastructure. Councils could already charge developers for infrastructure at greenfield sites through "development contributions".
The Prime Minister also warned that the Government would not be able to "sit back" if Auckland councillors did not deliver enough houses in the city.
Asked to elaborate, Mr Key said ministers would make announcements in this area soon.
Housing Minister Nick Smith has indicated that the Resource Management Act will soon be amended to allow ministers to force councils to free up land for housing.
Auckland's housing shortage has led to reports of a rise in people living in their cars or in garages.
Mr Key said it was difficult to tell whether the number of homeless in New Zealand was growing.
He had been advised that 428 people had told Work and Income New Zealand (WINZ) that they were homeless in March, but the data had gaps because it relied on self-reporting.
"A lot of what we see is anecdotal," Mr Key said. "[It] doesn't mean there aren't bigger numbers, I accept there may well be, but no one has absolutely perfect information on that."
The Government has allocated $41 million in the Budget for emergency housing.
Mr Key reiterated that anyone living in a car should report to WINZ, who would lobby on their behalf to Housing New Zealand.
Labour leader Andrew Little said many of the people living in cars were working but could not afford rents or a home.
Even desperate families were struggling to get onto waiting lists for state houses, he said.