It was the largest tragedy for the Baltic state since it regained independence in 1991. Latvia's government declared three days of mourning starting Saturday.
The rescue agency could not say how many people might be trapped under the rubble in the densely populated, working-class neighborhood between downtown Riga and the city's airport.
The reason for the collapse was still not known, but rescue and police officials said workers had been building a garden on the roof as part of the supermarket's original design. Riga Mayor Nils Usakovs told reporters that large bags of earth and sand on a weak spot on the roof could have caused the collapse.
An enormous crater-like hole gaped in the supermarket's roof, while building materials were still stacked on the remaining sections.
Rescue workers kept up their round-the-clock search for possible survivors as darkness fell on Friday, periodically turning off all equipment and asking the relatives of missing people to call so they could pinpoint ringing phones. Dozens of firefighters carefully sifted through the rubble.
Rescue agency spokeswoman Viktorija Sembele said the search for survivors was proceeding slowly, since both the rubble and the remaining sections of the roof were fragile and could easily collapse further if the wrong piece was moved.
About 500 square meters (5,300 square feet) of the roof collapsed, the rescue service estimated, destroying large sections of the store's high walls and nearly all its front windows.
Several large construction cranes gingerly hauled metal slabs and other debris from the central hole, while bulldozers cleared paths into the store. Sembele said approximately one-third of the rubble still needed to be removed.
The building was completed in November 2011. The Lithuania-owned Maxima was reportedly renting the space.
Maxima officials refused to comment, saying they would release a statement later.