But an economist said urgent measures were needed "overnight" and the failure to act now would spark a new run on investment property by "uninformed, under-capitalised investors".
In an unusually direct comment on immigration policy, Spencer told the Government to review the number of people moving to New Zealand, as the impact of high net migration on housing could not be ignored.
Record net migration was a key driver to surging housing demand, he warned. "Like taxation of investor-owned housing, migration policy is a complex and controversial issue," Spencer said.
"However, we cannot ignore that the 160,000 net inflow of permanent and long-term migrants over the last three years has generated an unprecedented increase in the population and a significant boost to housing demand."
It was impossible to "fine-tune" the overall level of migration, he said. "However, there may be merit in reviewing whether migration policy is securing the number and composition of skills intended."
Spencer warned that immigration adjustments would only work "at the margins", but they could, over time, help to calm the housing market.
Immigration Minister Michael Woodhouse was unavailable to comment last night and a spokesman for Key said he would not comment until later today.
The Government has previously ruled out changes to immigration levels, saying high net migration was strongly influenced by returning Kiwis and Kiwis choosing to stay.
Labour's finance spokesman, Grant Robertson, said that after the Government's repeated demands of the bank, it was now pushing back and telling National to play its part.
"In the diplomatic wording of the bank [this] is a shot across the bow to a Government that isn't doing anything tangible," he said.
The bank tightened loan-to-value (LVR) restrictions in November, making banks demand 30 per cent deposits for a mortgage secured against Auckland investment properties.
BNZ chief economist Tony Alexander said the bank should have introduced even stricter limits overnight.
Failing to do so would just cause a new run on investment property, he said. "I think they'll conclude in three or four years' time that maybe they should have brought the hammer down far more rapidly, before a whole lot of uninformed, under-capitalised investors got into the market."
Alexander wanted banks to demand 50 per cent deposits from investors in Auckland and 30 per cent from other buyers.
New Quotable Value data this week showed national house prices were rising at their fastest in 12 years. The prospect of stricter lending rules was cited as a reason for increasing investor activity.
The NZ Property Investors' Federation said new restrictions on investors would increase rental prices and reduce rental supply.
Bharat Bhushan and his partner Lovely Garg are still looking for a house in Auckland and Bhushan does not think the Reserve Bank's announcement will make the hunt any easier for them in the short term.
NZ First leader Winston Peters said: "The Reserve Bank and Auckland Chamber of Commerce both suggest 13,000 new homes must be built [in Auckland] every year to meet demand.
"The latest plan of the Government will not work unless immigration is curbed."
