Danish Culture Minister Jakob Engel-Schmidt said it was touching to see how many people lent their hand "to save art treasures and iconic images from the burning building".
Brian Mikkelsen, chief of the Danish Chamber of Commerce, which is headquartered in the Old Stock Exchange, and his staff were seen scrolling through a binder with photos of paintings to be saved.
Denmark's culture minister lamented the inferno was a "national disaster". (AP PHOTO)
"It is a national disaster," Mikkelsen told reporters.
The fire began on Tuesday morning in the copper roof of the Old Stock Exchange, or Boersen, spread to much of the building and the roof, parts of which also collapsed, and destroyed the building's interior, firefighters spokesman Jakob Vedsted Andersen said.
Firefighters who reportedly pumped water from the nearby canal were seen spraying water through the doorway of the Old Stock Exchange's gilded hall that is used for gala dinners, conferences, parties and other events and where many of the paintings hung.
The cause of the fire was not immediately known.
The building, which is next to the Christiansborg Palace where the parliament sits, is a popular tourist attraction and has been photographed millions of times.
The Old Stock Exchange was being renovated when the blaze ripped through the building. (AP PHOTO)
Its distinctive spire, in the shape of the tails of four dragons twined together, reached a height of 56 metres.
Huge billows of smoke rose over downtown Copenhagen and people were seen rushing inside the building to save paintings.
Ambulances were at the scene but there were no reports of casualties.
A spokesman for the company working on renovating the building said the carpenters who worked on the roof had all come out.
King Frederik wrote on Instagram that "they woke up to a sad sight" of "an important part of our architectural heritage" being destroyed by the flames.
Locals pitched in to help carry artworks from the 17th-century structure. (EPA PHOTO)
Prime Minister Mette Frederiksen wrote that "irreplaceable cultural heritage" and "a piece of Danish history is on fire".
The building and the spire had been encased in scaffolding, which later collapsed in the fire.
The roof, masonry, sandstone and spire of Boersen - built in 1615 and considered a leading example of Dutch Renaissance style in Denmark - was being renovated, said the Chamber of Commerce, which moved into the building after Copenhagen's stock exchange left in 1974.
The adjacent Christiansborg Palace has burned down on several occasions, and most recently in 1990 a fire broke out in an annex of the Danish parliament, known as Proviantgaarden.
However, the Old Stock Exchange survived unscathed.
