Firefighter Barry Martin, aged 38, remains in Edinburgh Royal Infirmary with serious injuries and is currently in a critical condition.
Barry, from Fife, was one of five firefighters who suffered injuries in tackling the fire.
Four others were also transported to hospital and have subsequently been discharged. Two were treated for smoke inhalation and two for burns.
At its height 22 fire appliances were mobilised to the scene at Rose Street, with more than 100 firefighters working in difficult conditions to bring the building fire under control.
One fire appliance remains in attendance today (Tuesday, 24 January) to monitor the building for potential hotspots.
Interim Chief Officer Ross Haggart said: “This was undoubtedly a serious and complex fire.
“Our thoughts are very much with Barry and his family, and indeed with all of our colleagues who were injured in responding to this incident.
“Barry is a firefighter based in Edinburgh and we ask that everyone please respect his family's privacy at this time.
“We continue to provide all possible support to our colleagues and their families, as well as all staff involved.
“We are liaising with appropriate partners to ensure a full and thorough investigation is undertaken into this incident.”
Interim Chief Officer Haggart added: “Can I please take this opportunity to thank our dedicated crews and staff for their professionalism in responding to this challenging incident; also to our partners for their support on the ground yesterday.
“And of course our thanks go to the health professionals who provided and continue to provide treatment to our injured colleagues and continue to care for Barry.”