Mr Walters said the welfare of staff was the top priority, and teams had been moved to the council's Bledisloe and Hereford St buildings for several months while officials considered what to do with the site.
Tests are being carried out at the building, and a report due this week will help executives decide what the future of the site will be.
Mr Walters said it was not difficult to accommodate staff from the Three Kings building in other offices.
The fungus Stachybotrys chartarum, also known as black mould, grows in buildings with chronic water damage or serious leaks, and can produce toxins.
Allergy experts said black mould could have a wide range of health effects, and posed a greater risk to people who had infections or asthmatic conditions.
The mould was found in many of the buildings affected by Auckland's leaky home crisis, and a report commissioned by the council in 2007 found that exposure to it was associated with upper respiratory tract infection, coughs and asthmatic symptoms.
In a separate report, the fungus was also linked to rashes and breathing problems among homeowners.
The greenish-black mould was said to be not harmful when it remained within walls or sealed areas, but could affect people if it spread.
The Department of Building and Housing said that while the mould was growing and still wet, a slime covered the growth and prevented its spores from getting out.
But when the mould dried, its spores became airborne.
Mr Walters said the future of the Three Kings council building had been under discussion before the mould was found.
"We've inherited all sorts of buildings all over the region, and now we're getting to grips with which ones we need and which ones we don't need. [The mould investigation] will all be part of the mix."
BLACK MOULD
(Stachybotrys chartarum)
* Greenish-black mould which grows in water-damaged homes and can produce toxins.
* Exposure to the fungus can cause chest infections, rashes or breathing difficulties, particularly among people with respiratory problems.
* In Auckland, 170 leaky homes were found to have the mould, and some inhabitants reported illness as a result.