Mr Key said that if land prices in any region were going up too quickly, the local council would have to free up more land.
"If they don't do that, they will breach the law," Mr Key said.
The statement would include specific thresholds for growth which would trigger a requirement to allocate more land for residential development.
Mr Key would not reveal details about the thresholds, but Finance Minister Bill English has previously suggested that councils could be forced to act if the median house reached 10 times the median income.
"It will be a very clear signal," Mr Key said.
The Prime Minister pointed to a landmark Supreme Court case in 2014, which ruled that an NPS took priority over "the protective element of sustainable management".
That had implications for an NPS on urban development, he said.
If a council did not agree to rezone land to "residential" to allow a housing development in a growing area, and a developer challenged the council in court, "the developer will win".
Mr Key said the Government would have to provide support for infrastructure to allow developments to go ahead - one of the major obstacles to housing supply in Auckland.
"We are quite happy to step up and support the infrastructure whether it be schooling or roading."
Questioned about the Auckland Council's ability to fund the new growth given high debt levels Key said "there were other ways to fund these things".
Asked if they should sell assets he said: "They could do."
The NPS will not require a law change.
The Government has previously tried to include urban development in the main principles of the Resource Management Act.
But it was repeatedly unable to get the support of its support partners, who were concerned that it would undermine environmental bottom lines.
That has prompted the Government to take an alternative route with a NPS, which does not require a Parliamentary majority to introduce.
The Labour Party recently said it would support the abolition of urban limits in Auckland.
