Mr King said he had replied to the minister's request saying: "We would endeavour to do that when it comes to the sign-off."
One of Labour's key election policies was building affordable housing for first home buyers.
SHAs are intended to fast-track more new homes and allow building on land that may not be zoned residential.
The news of a 40 per cent minimum left Councillor Mark Bunting rattled at the council meeting. Last year he attempted to put a target of 20 per cent affordable housing into the policy.
"Why is it now a good idea to a allocate certain amount of affordability when only (Councillor) Dave Macpherson and I thought it was originally," Mr Bunting said.
"Apart from the KiwiBuild, why are we so enthusiastically embracing it now? What has changed?"
Mr King told Mr Bunting he would do whatever he could to work with central government and do what he could to help the government of the day achieve their goals.
"The government has asked us to meet a 40 per cent threshold. This council signs off on SHAs and I would expect this council wouldn't sign off on anything below 40 per cent," Mr King said.
In October last year council approved six special housing areas to move to the next stage of development, but only two of those applications had a target to build affordable dwellings in their proposal.
All six will now have their applications viewed in March under the policy introduced last year, but will be aware that both local and central government would be unlikely to sign off if a target of 40 per cent of affordable dwellings was not met.
HCC general manager for growth Kelvyn Eglinton said that the current applications will be brought forward under the current policy while they wait for central government to give a confirmed policy position over what the affordability target is.
The mayor said he contacted all six personally and had indications they would be able to meet the 40 per cent minimum.
Mr Eglinton said that the current applicants would be able to meet the target with smaller foot print houses.
Councillor Siggi Henry was concerned at how the houses would be built to cater for affordability and whether they would be of a poor living standard.
"They say healthy and all of this but really it is just junk again, cheap junk builds," Ms Henry said.
Mr Eglinton said quality aspects are driven through the building code.