The Government was not considering further demand-side measures, such as removing tax incentives for investors, a ban on foreign buyers, or extending the "bright line test" beyond two years.
But the Government would not stand in the way of new controls by the Reserve Bank "if they made sense", Key said.
This included debt to income ratio limits. Key said the Government would back the bank's governor Graeme Wheeler if he proposed the measure.
The bank is currently investigating whether the limits would help to cool the overheated housing market, which it sees as a risk to the New Zealand economy.
Labour leader Andrew Little said the Government should not be leaving the job of controlling demand to the Reserve Bank.
"If we're going to get serious about people owning their own home then just relying on the Reserve Bank isn't enough."
Little said debt to income ratios were "a last, desperate measure" by the central bank which was getting no help from the Government.
He was concerned that the policy could have a disproportionate impact on first-home buyers, and said the Government should focus on building more affordable houses instead.
Debt to income ratios are already used in the United Kingdom, where most buyers cannot get a mortgage higher than 4.5 times their annual earnings.
If applied in Auckland, it would limit a typical family to a mortgage of no more than $400,000.
