Rescue workers cleared away rubble from the store, which had occupied around 1,500 square metres (5,000 square feet), as ambulances and fire engines stood by.
Police said the death toll had reached 38 as of 1230 GMT, including three rescue workers. Thirty eight more were injured.
“In the past hours no survivors have been found,” said Viktorija Sembele, a rescue service spokeswoman.
Latvian public television said as many as 40 people could still be trapped in the rubble, based on information from security cameras, but Sembele could not confirm the figure.
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 located about a 30- minute drive from the 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 from Saturday and said the collapse had shattered Latvia, a former Soviet republic which joined the European Union nearly a decade ago and will join the euro zone next year.
“In our thoughts we are together with all those stricken by this tragedy,” Dombrovskis said. “No matter what the cause of the tragedy is, the number of victims is too big.”
Among other post-Soviet disasters to hit the country of two million, 23 Latvians perished along with about 800 others in 1994 when an Estonian ferry sank in the Baltic Sea. Twenty six people died in 2007 in a blaze at a Latvian care home.
HOPE
Earlier on Friday, 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 told Reuters Television. He said he believed his wife was alive.
A girl at the scene told public radio 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 yet found her mother.
Other witnesses said there was a loud noise and the store went dark. People escaped through holes in the windows.
Rescue workers were called late on Thursday to the store, which according to local media had been awarded an architecture prize when it was completed in 2011. 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.”
Source: Bd news24