"My ambition is to try and have sufficient special housing areas approved by Christmas for at least 5000 additional homes."
Mr Brown said the council was already issuing consents for new homes at a faster rate than a year ago.
"We've got some real pace around the housing build and I'm very confident we'll be able to achieve the first year's target and the following year's target ... but we really hope the special housing areas will provide a real impetus to the market."
The council had received 70 to 80 applications or expressions of interest from developers for fast-tracked consents.
However, while the council wanted to announce the first special housing areas this month, "obviously we are going now into election mode and it's important for us not to overly tax the councillors".
Dr Smith said the consenting process for homes in special housing areas would take six months at most. Infrastructure works would take no longer than a further six months, with construction beginning after that.
The unitary plan identifies the need for 400,000 new homes to keep up with population growth in the city over the next 30 years. Dr Smith said the Government's deal with the council would enable the "least contentious 39,000" of those houses to be built over the next three years.