Work on the courthouse started in October, but the level of activity has picked up in recent weeks, after heavy machinery, including a large drill and concreting equipment, was brought on to the site.
A Ministry of Justice spokeswoman said demolition work was under way to open up parts of the interior so that earthquake strengthening work could begin.
''Four bore holes have also been drilled as part of ongoing geotechnical testing of the ground which is related to tower strengthening work,'' the spokeswoman said.
The work was on schedule.
The Otago Daily Times understands that all the floors in the building have been removed and are to be replaced with concrete, with original floorboards placed on top.
When the project was given the go-ahead in September last year the aim was for work to be completed this December.
Amalgamated Builders managing director Richard Johnston said at the time the project would involve about 38 fulltime staff and close to 50 sub-contractors and suppliers.
Most contractors would be sourced from Dunedin.