The minister wants to see houses being offered to first home buyers in the city for below the median house price of just under $540,000.
Mr King is proposing changes to the special housing legislation which council signed off on August last year.
The changes would include putting in a requirement of 40 per cent of affordable housing in new builds.
The builds would then only be offered to first time home buyers or those who qualify under the central government's legislation.
Councillor Angela O'Leary was in support of the affordable housing move but signalled that she wanted central government to make sure they do their part.
"Government has a lot of catch up on the previous government in terms of a lot of the housing shortfall in my opinion and the opinions of other," Ms O'Leary said.
"I wouldn't want us to carry that financial burden in going down this route."
Council will also ask for a two-year extension of their Special Housing Accord while central government works on its legislation.
Councillor Garry Mallett said that the current district plan is now completely worthless thanks to the Special Housing Accord.
"When are we going to accept that our current district plan is completely unfit for purpose?" Mr Mallett said.
Chief executive Richard Briggs said there may be a time when the district plan may need to adapt for the future.
Mr Mallett then raised the concerns of residents who are against infill.
"There is a job that needs to be done. These people don't like the thought of kids not having green space to run around in at home."
One of Labour's election promises was to deliver on its KiwiBuild policy which is to build 100,000 affordable houses over 10 years for first home buyers.
KiwiBuild homes will only be sold to first home buyers. To avoid buyers reaping windfall gains, a condition of sale will require them to hand back any capital gain if sold on within five years.
