The Scottish Fire and Rescue Service said more than 90% of the structure was viable and they had protected up to 70% of the contents.
The culture secretary said everything must be done to restore the building.
A church service is due to be held at 16:00 for those affected by the fire.
The ecumenical gathering will take place at Renfield St Stephens in Bath Street.
Culture Secretary Fiona Hyslop told BBC Radio's Good Morning Scotland programme: "The important thing is to make sure this building can be restored to its full glory.
"Just how we do that will depend on assessment of the immediate works.
"This is an internationally renowned building and I'm absolutely confident that we can rely on the interest in, and supporters of, Charles Rennie Mackintosh to make sure that we do everything we can."
Ms Hyslop said firefighters had carried out "quite a remarkable job".
"They worked tirelessly to try to protect this iconic building, so important to Scotland and so important to the world," she added.
Fire broke out at the listed building at about 12:30.
Eyewitnesses said the fire appeared to have started when a projector exploded in the basement of the building on Renfrew Street in the city centre.
Everyone who had been in the packed building was said to have escaped safely.
Final year students had been preparing for their end-of-year degree show in the building when the blaze broke out.
The main blaze was extinguished by about 17:00 but there were still pockets of fire within the building.
The Mackintosh building, completed in 1909, is "unique" in that it is a working art school as well as a work of art.
It has an A list rating, meaning it has been classified by Historic Scotland for its age and rarity.
From the facade to the fixtures and fittings every detail shows the craft of Charles Rennie Mackintosh, Scotland's most-lauded designer.
It is not yet known how much damage has been caused to the building's library, recognised as being one of the finest examples of art nouveau in the world .
In a statement issued at 21:30, Assistant Chief Officer Dave Boyle said crews had been working "absolutely flat out" in an effort to save "this treasured building and many of the items it housed".
He said: "While the priority from the outset was to save life we have also been working closely with Glasgow School of Art staff to ensure firefighters conducted an effective salvage operation.
"We are of course very conscious the Mackintosh is a world-renowned building that is a key feature of this great city, and that the artworks it stores are not only valuable but also cherished."
ACO Boyle added: "We are acutely aware this period is the culmination of years of endeavour for students and that their irreplaceable work is inside the Mackintosh.
"Work to save everything that can be saved is ongoing and we will continue to work closely with GSA staff and students throughout this operation."
Fire crews arrived on the scene within four minutes of the alarm being raised.
Search and rescue teams entered the building wearing breathing apparatus and led a number of people to safety. There were no reports of any casualties.
Police cordoned off Renfrew Street, and smoke was also drifting across the M8. Large crowds of students and onlookers gathered near the scene, with several people in tears as they watched the events unfold.
Fire appliances from across Glasgow were joined by specialist crews from other areas of Scotland, with firefighters seen pouring water on the building from a high ladder as flames blew windows out.
Hugh Thornhill, a second year student, said: "I was helping one of the fourth years set up their exhibit and suddenly the alarm went off.
"We didn't think it was anything but we had to go out and then we saw smoke coming out and realised that it was really bad. It got to the point where flames were coming out of the top floor.
"All that effort is gone, everyone's work on that side of the building is ruined. Even if it didn't catch fire it will be damaged extensively.
"The degree show next month is pretty much a bust now, it's sad."
Broadcaster Muriel Gray, a former student and current chairwoman of the school, arrived and burst into tears when she saw the building in flames.
Ms Gray told BBC Scotland she was "heartbroken" to see the "most amazing building in Glasgow" go up in flames.
Speaking later, she added: "It has been a devastating day for everybody involved in Glasgow School of Art. We want to make it clear we are so grateful to the fire service. It's a very black day."
Asked how the building could be restored, Ms Gray said: "We don't know what's been destroyed. It's a waiting game."
Scotland's First Minister Alex Salmond said on Twitter: "Thoughts with staff & students at @GSofA - awful to see destruction of this iconic building and students work."
Austin Yuill, who works as a chef at the art school, told the BBC: "I was moved two streets away from the Mackintosh building but before we left the place was completely ablaze all down the west side of the building.
"I'm told it started in the basement and it's worked its way all the way up through the five floors.
"As far as I know it started from a spark which has gone on to foam, expanding foam."
Asked how busy the art school was, he said: "It would be very busy because we're working up to the end-of-year assessments, so all the students were installing their work today all over the Mackintosh building. There are a lot of very upset students here."
He added: "Quite apart from it being voted the best building of the last 175 years, it is a major tourist draw and has an incredible reputation as an art school. This is really terrible."
Charles Rennie Mackintosh is lauded as Scotland's most influential architect and designer, with the art school building which bears his name considered by many to be his greatest masterpiece.
Mackintosh was a 28-year-old junior draughtsman at a Glasgow architecture firm when he drew up the designs for the building, which features distinctive heavy sandstone walls and large windows.
The dramatic art nouveau design took about 12 years to be completed, opening in 1909, but it signalled the birth of a new style in 20th Century European architecture.
The president of the Royal Incorporation of Architects in Scotland, Iain Connelly, said the value of the building "goes well beyond Glasgow or even Scotland".
He added: "It is a work of architectural heritage of world renown and its influence on 20th century architecture is immeasurable. Scotland has seen the loss of an international treasure which reflects the genius of one of our greatest ever architects."
In recent years, Glasgow School of Art has produced many of the UK's leading contemporary artists such as Douglas Gordon and David Shrigley and three recent Turner Prize winners: Simon Starling in 2005, Richard Wright in 2009 and Martin Boyce in 2011.
Other former students include actors Robbie Coltrane and Peter Capaldi and artist Peter Howson.
Firefighters battling the blaze at Glasgow School of Art's Mackintosh building say they have prevented the destruction of both the structure and the majority of its contents.