Wellington mayor Justin Lester says there is a "reasonably strong likelihood" that they may deconstruct the at risk building on Molesworth Street, following the 7.5 magnitude earthquake on Monday.
The building has been described as "seriously structurally compromised".
Cordons remain in place in parts of Wellington's CBD and an apartment on Tennyson Street has been evacuated. A number of government buildings remain closed.
Mr Lester says that the buildings the council deems to have serious damage are now in "single digit figures".
Building Consents General Manager Mike Scott says the combination of quakes, flooding, and strong winds in the region have created a "perfect storm" but Wellington "has done incredibly well for such a significant earthquake".
New Zealand Defence Force (NZDF) headquarters in central Wellington, Freyberg House, is closed indefinitely due to earthquake damage.
In a statement, NZDF says the "full extent of the damage will not be known for several days, and until that assessment is complete we cannot determine what work will have to be done or when it will be possible to reoccupy the building".
The statement said the organisation is considering a range of options for the interim, including remote working and relocation of staff to other NZDF facilities.
60 residents were evacuated from an apartment building on Tennyson Street in Wellington's CBD.
Residents from the building told Newshub a fire alarm went off at 11:40am, they were told there were cracks in the building and they had to leave.
The building has structural damage "like a broken bone" assistant fire service area commander Gareth Hughes says.
(Tennyson Street, Newshub)
Mr Lester says if residents from Tennyson Street are unable to find accommodation with friends and family, the city council will be able to provide for them.
"We've got partnerships across the city", he says, including at student accommodation facilities.
Pipitea Street is also closed due to concerns about the facade of Pipitea House, Wellington City Council says.
A number of carparks are also closed until they have been assessed, including on Clifton Terrace, Harris Street, Courtenay Central, Molesworth and James Smith, Mowbray off Bolton Street, Gilmer Terrace, Midland Carpark, Lombard Street, Marion Street, Left Bank, Ballantrae Place, Stout Street, and Lower Tory Street.
The area around the Deloitte building on Molesworth Street remains closed to pedestrians and traffic at the Hill St and Hawkestone St intersections with Molesworth St, making several other buildings inaccessible:
A building on the corner of Manners St and Taranaki St is cordoned off due to a risk of falling glass, and despite the damage done to it by the quake, the fire service says there's "no imminent risk" of collapse.
Staff have been locked out of Statistics House for at least 12 months after a floor pancaked in the 11-year-old building, while the CentrePort BNZ building suffered cracks and broken glass.
Property Council New Zealand Wellington president Mike Cole is optimistic about Wellington's situation.
"It's maybe a learning experience after Christchurch. Engineering, like a lot of other professions, they progress along a certain way then an event happens like in Christchurch and you see what works and doesn't work - it is a little bit unusual that it affects new buildings in that way," he says.
Mr Cole insists Wellington's building code is up to standard.
"The public should have confidence in Wellington's building stock. Walking downtown yesterday, it was actually evident the buildings I was walking past - how many have been strengthened or were a good standard before Christchurch anyway. Overall the city is pretty good."
But Wellington Central MP Grant Robertson is concerned with how buildings in the area built on reclaimed land have responded in recent quakes.
"A number of departments and banks have moved there over the years - I think in the medium term, that does need some reconsideration," he says.
Newshub.
