The technical room is located on the ground floor of the Assembly compound.
Staff and other workers are currently leaving their offices to avoid being trapped as smoke fills up the walkways.
Senators who were initially seated in the gallery area have also moved out.
The cause of the fire is not yet known.
Staff is making attempts to put out the fire with fire extinguishers.
One staff member familiar with the technical room said the fire started at where air conditioners units serving the assembly are kept.