There was a loud bang as the brickwork came down and a cloud of ash enveloped the building.

"The thing we feared has happened," Copenhagen fire department chief Jakob Vedsted Andersen told reporters.

The outer wall in the half of the building that burned on Tuesday collapsed entirely.

Parts of the top of the wall around the grand entrance to the Bourse also crumbled to the ground.

"About 40 to 50 per cent of the facade in the half of the building that caught fire has collapsed," Copenhagen fire department incident manager Tim Ole Simonsen told reporters.

There were no injuries, the fire department said.

Tuesday's blaze toppled the spire of Copenhagen's Old Stock Exchange and collapsed a large part of the roof, in scenes reminiscent of the fire that engulfed the Notre Dame Cathedral in Paris in 2019.

Simonsen said the walls had been exposed to huge physical stress over the past few days as their supports burned away, they were heated to incredible temperatures then cooled again, and exposed to water.

Firefighters had worked through a second night to quell flames in the basement and smoke was still rising on Thursday as attention began turning to the building's restoration.

The Danish Chamber of Commerce, which owns the building and uses it for its headquarters, has vowed to rebuild the exchange which originally opened as a commodities trading venue in the 17th century.

Copenhagen Mayor Sophie Haestorp Andersen said she would travel to Paris next month to learn about Notre-Dame's restoration.

Police have said it could take months to determine the cause of the fire.

No one was hurt in the blaze.

Anders Ellegaard of Denmark's forensic centre told TV2 that experts would help determine whether police could pursue a criminal case.

Australian Associated Press