Other 17 people were injured in the collapse and emergency services recovered two bodies from the rubble.
The cause of the collapse is not known, but Riga’s deputy mayor Andris Ameriks is quoted as saying it might have been caused by an explosion.
There are conflicting reports of what might have caused the collapse, with reports of an explosion and other suggestions that a garden was being constructed on the roof.
The 500 sq m store run by the Maxima chain was built in 2011, say reports.
Fire and Rescue Service spokeswoman Viktorija Sembele said one firefighter was among those killed, and seven were injured after another portion of roof fell on rescue workers as they searched for survivors, reported the Associated Press news agency.
Local media say a “winter garden” was being planted on the roof using sand which had become sodden with rain.
Emergency services have recovered two bodies from the rubble.
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