At least 32 people have died, including three firefighters, after an enormous section of roof collapsed at a Latvian supermarket in the country's capital.

The reason for the collapse during shopping rush-hour on Thursday was still not known but rescue and police officials said that possible theories include building design flaws and poor construction work.

Pictures from residential buildings overlooking the store in Riga showed an enormous crater-like hole in the roof. Building materials were stacked on remaining sections of the roof, where workers were building a garden as part of the Maxima supermarket's original design plan.

Thirty-five people were injured, 28 of whom were taken to hospital, including 10 firefighters, the Fire and Rescue Service said. It could not say how many people might be trapped under the rubble.

Several large construction cranes hauled debris from the hole, where firefighters slowly sifted looking for survivors.

Rescue workers periodically turned off all equipment and asked relatives of missing people to call so that they can pinpoint ringing phones. Work was continuing slowly since both the rubble and remaining sections of roof were like a house of cards and could easily collapse further if a wrong piece is moved or lifted, said an official.

Firefighters suffered casualties when large sections of roof fell on them right after their arrival on the scene.

The rescue service estimated that approximately 500 square metres of roof collapsed, destroying large sections of the store's high walls and nearly all its front windows.

The building was completed in November 2011. The Lithuania-owned Maxima was reportedly renting the space. Maxima officials refused to comment and said that they would release a statement later.

The supermarket is in a densely populated district between central Riga and the city's airport.