The roof caved in late on Thursday when the 50,000 square-feet complex was filled with people shopping after work.
Among those killed were three rescue workers. At least 38 people were injured.
“In the past hours, no survivors have been found,” Viktorija Sembele, a rescue service spokeswoman, said.
To help rescuers look for people in places where shoppers actually were during the collapse, police have created a map based on tapes from security cameras.
Latvian public television said as many as 40 people could still be trapped in the rubble, based on information from the cameras, but neither Ms Sembele nor police could confirm that figure.
“Every hour, air temperature, high air moisture – they are factors that reduce possibility of finding any survivors. But, of course, hope always remains,” Armands Plorins, chief of the emergency ambulance service, said.
The cause of the collapse remains unknown, but interior minister Rihards Kozlovskis said: “It is clear that there has been a problem with fulfilment of construction requirements.”
Local media said workers had been building a roof garden on the supermarket, a single-storey building built in 2011 and a 30- minute drive from Riga city centre. Soil, grass and parts of a new walkway could be seen dangling from the edges of the collapsed rooftop.
Prime minister Valdis Dombrovskis announced three days of mourning and said the collapse had shattered Latvia, a former Soviet republic which joined the European Union nearly a decade ago and will join the eurozone next year.
“In our thoughts we are together with all those stricken by this tragedy,” Mr Dombrovskis said. “No matter what the cause of the tragedy is, the number of victims is too big.”
Earlier yesterday, about 50 people gathered near the ruins for news of relatives, while others brought candles and flowers.
“I have a wife there. There is no information about her, whether she is dead or alive. Wherever I call, there is no information,” Igor Umanov said. He said he believed his wife was alive.
A girl at the scene said she had gone into the shop with her mother when a concrete block collapsed between them and that she was nearly buried in rubble. She managed to escape but had not found her mother.
Other witnesses said there was a loud noise and the shop went dark. People escaped through holes in the windows.
Rescue workers were called late on Thursday to the supermarket, which local media said had been awarded an architecture prize when it was first built. Several were injured by a second collapse because of the building’s weakened structure.
Rescue workers were halting work periodically to listen for survivors and for the sounds of mobile phones in the wreckage, Latvian television said.
State fire and rescue service chief Oskars Abolins told Latvian TV that heavy concrete blocks were hampering rescue efforts, adding: “As we have to search all the rubble and the whole construction, rescue work might continue for another day.”