Several rescue workers are among the dozens of people who died as the roof of a supermarket collapsed during shopping rush hour in the Latvian capital Riga.

The lifeless bodies of 32 people have been pulled from the rubble of the 550 sq m (5,380 sq ft) Maxima supermarket in an eastern suburb of the city but the death toll is expected to rise, officials said.

"Three of them were state fire and rescue service officials," Latvian rescue services spokeswoman Viktorija Sembele said.

Firefighters who rushed to the premises after the collapse were trapped under the rubble after a second part of the roof broke down.

At least 35 people were injured, 28 of whom were hospitalised, including 10 firefighters.

The reason for the collapse is still unknown but Latvian Interior Minister Rihards Kozlovskis said it was clear a failure in the fulfilment of construction requirements occurred.

The construction of the one-storey supermarket was completed in November 2011 but workers were still building a rooftop garden.

Authorities said they have launched a criminal investigation.