The Northern Ireland Fire and Rescue Service say crews responded to a report of a fire in a flat on the 8th floor of the Russell Court Building on the Lisburn Road.
Extra resources were mobilised to the incident on Wednesday night because of the extent of the fire..
A spokesperson said: “Firefighters wearing breathing apparatus used two jets and two thermal imaging cameras and small tools to deal with the fire.
“Two dogs died at this incident.
“The cause of the fire appeared deliberate.”