The properties at 380-394 Princes St and 11 Stafford St are owned by Totara Dunedin Properties and the buildings are being demolished by Scope Group.
The Stafford St building is being demolished to provide site access necessary for demolition equipment.
"The demolition of 11 Stafford is going slowly as it requires careful hand demolition so that the adjacent building is not compromised," a project spokeswoman said.
"This requirement for manual demolition has pushed the completion date back until the first week of March 2024 for site handover from Scope Group.
"This means that traffic management on Princes St will be in place for longer than originally anticipated, and we apologise to residents for any disruption."
In September, before the project had started, it was anticipated demolition could take 10 weeks.
There was then a delay because of what was described as unanticipated administrative issues and on November 1 a large portion of facade masonry collapsed into the building zone.
The first stage of work to lower the height of 380 Princes St’s facades was now complete, the spokeswoman said.
"This work was necessary to remove the risk of debris falling outside the cordoned-off site fencing area.
"Demolition materials must now be removed from behind the facade walls back into the demolition site rather than using the Princes St exit."