Wellington City Council has taken over management of the deconstruction of 61 Molesworth St from the building's owner Prime Property Group.
The council had taken over management of the site so that the deconstruction could happen as quickly as possible, said building consents and compliance manager Mike Scott.
Council will be working with support from specialist demolition companies.
Costs for the deconstruction would be recovered from Prime Property Group and their insurance company, Scott said.
"To ensure public safety, this work must be completed as quickly as possible, and that's one of the main reasons we're taking over management of the building."
Council spokesman Richard Maclean said Prime Property was a small company.
"In reality they are not designed to deal with emergency building demolition," he said.
"We've got way more resources to throw at it."