The blaze that ripped through the 400-year-old landmark, toppling its spire in a scene reminiscent of the 2019 fire at Paris' Notre-Dame Cathedral, was still burning in some hard-to-access places.
Roughly half the Dutch Renaissance-style building was saved, although massive damage still occurred as fire fighters had drenched it in water.
"Everything that was once part of the storey partitions and building structures inside has been burnt away," Copenhagen fire department Operations Chief Frank Trier Mikkelsen told Reuters, referring to the part of the building worst hit.
"Only the outer walls remain, leaving an empty shell."
Emergency services were joined by passers-by on Tuesday in carrying large paintings away from the building shortly after the fire broke out in a race to save historic artefacts from the flames.
"There are probably a thousand objects in there but the things I would say are the most important have been saved," Brian Mikkelsen, CEO of the Danish Chamber of Commerce which owns the building, told public broadcaster DR.
He said employees and firefighters knew what to get out as they already had a "worst case" emergency plan in place.
Putting out the fire was taking longer than expected due to lingering pockets of flames found in the rubble and the work was expected to last at least until Thursday morning.
Large containers had been installed overnight to support damaged walls and prevent the historic brickwork from collapsing, fire officials said.
The building no longer houses the stock exchange but serves as the Chamber of Commerce headquarters.
