Demolition work is entering its third day at the quake-damaged building at 61 Molesworth St in central Wellington.
Work began on Monday after being postponed over the weekend.
The building was deemed unfit for purpose after sustaining structural damage in the magnitude 7.8 Kaikoura earthquake on November 14.
A crane is removing the top storeys and main structure of the building, and the demolition process will take between 10 and 14 days.
Wellington City Council hopes to be able to reopen at least part of Molesworth St before the Thorndon Fair takes place nearby on December 4.
"Optimally we'd like to be open at least one lane on Molesworth St before that, so the fair's not going to be negatively impacted", building consents general manager Mike Scott says.
The fair attracts around 20,000 people each year, and Molesworth St is an access route the Tinakori Rd and Hill St event.
A number of buildings around the condemned structure remain closed.
"I'd like to think that by the end of this week we'll in a much better position to give them absolute clarity about when they can come back in," says Mr Scott.
Despite the damage to several Wellington buildings after the November 14 earthquake, Prime Minister John Key says government departments will not be moving out of the capital.
He says State Services are now looking for temporary locations for people from the damaged defence and Inland Revenue Department (IRD) buildings.
"It depends how long they're out of the building for," he told the Paul Henry programme on Monday.
Defence House, the IRD building and the Statistics New Zealand building are all relatively new, he says, and buildings in the capital have a "higher code" for construction.
"The worrying thing is that these are the buildings that showed some damage.
"But it depends on the intensity of the earthquake at a particular place, and the fact that something is built to a high code doesn't mean there isn't damage, it just means that you can get out of it alive."