There are now four buildings at Wellington's CentrePort which could be demolished following the 7.8 magnitude earthquake.
The Statistics New Zealand Building is already under investigation for its poor earthquake performance.
Now it has been announced that Shed 35, a vacant cargo store, has sustained serious damage.
The 1915 building is heritage-listed and has been vacant for many years because of its earthquake prone status.
CentrePort chief executive Derek Nind said options for the building include demolition.
Two warehouses on Aotea Quay will also be demolished, although their removal was already earmarked before the quake.
CentrePort said it is working closely with Wellington City Council and other stakeholders on various options for the affected buildings.
"We've got ferries, fuel, logs, cars, and cruise ships operating successfully and we're working on solutions for our container service," Nind said.
"Nevertheless, we have sustained significant damage across the port and are working closely with Wellington City Council and others on various options for our port buildings, which includes potential repair through to removal."
Meanwhile the British High Commission building remains closed.
The office in Thorndon is closed for safety reasons, but in the interim the Commission will be operating consular services from the Australian High Commission at 72-76 Hobson St.
The Commission's contact details have not changed.
British people requiring emergency travel documentation are encouraged to go to the online booking system. Most emergency travel documents will need to be issued by the Auckland office.