Staff at Rhondda Cynon Taf Council's office in Clydach Vale were evacuated following concerns about a landslip.
ITV Wales reporter Rob Osborne, who was at the scene, said around 200 workers were moved from one part of the site to another.
A spokesperson for the council said an engineers' assessment was carried out after the evacuation, which confirmed there was no danger to the general public or any buildings.
Continuous heavy rain from storms Ciara and Dennis has caused major flooding and landslides in parts of Wales over the past few weeks.
Hundreds of people have been forced to evacuate their homes due to the extreme weather.
Mr Drakeford said: "We agreed we would jointly convene a meeting as fast as we were able - bringing all of the different responsible authorities together and if there is further remedial action that is necessary to get a full picture and then a plan to respond to that."
A yellow weather warning for rain is in place in parts of north and south Wales until 2pm on Thursday.