Time was running out to find survivors on Thursday as rescuers continued to work in the Kumamoto area on Japan 's southern main island of Kyushu, where the magnitude 7.1 earthquake hit Tuesday.
The number of those missing was unclear.
The quake left at least 63 people injured, five of them seriously, the Kumamoto prefectural government said.
Chief Cabinet Secretary Minoru Kihara, speaking to reporters Thursday, gave a higher number for the death toll at 28.
That came from a police tally, he said, which included cases still under investigation.
Some of those cases might later turn out to be unrelated to the earthquake.
Survivors spoke about coming home and desperately pulling family members out of the wreckage.
Some had suffered injuries and were rushed to the hospital.
Thousands of people spent another night at evacuation centres set up throughout the area in gymnasiums and other big spaces.
Some homes were still without water or electricity, while others were simply afraid to go back.
Almost 23,000 homes were still without electricity and more than 10,000 people were staying in the roughly 400 shelters, where power sources were being added to provide air-conditioning.
Concerns were growing about illness, including from the sweltering heat. The Ministry of Environment sent out a heat stroke alert for the Kumamoto area, with temperatures expected to reach as high as 33C on Thursday.
Although Japan boasts strict building codes because of the frequency of quakes in the country, some homes in the area are in the older style of Japanese housing, making them relatively fragile.
The most serious damage was at the Aeon shopping centre in the town of Kashima, which was bustling with thousands of people when the quake struck in the late afternoon.
The company said some 3000 customers were evacuated to a parking lot before the explosion happened in another part of the mall, where some people were still working.
The centre's second floor collapsed, trapping people.
As of early Thursday, six people were confirmed to have died at the mall site among the 11 people pulled out of the wreckage, according to Kumamoto authorities.
Family members of those still missing could be seen wandering helplessly near the wrecked mall, waiting for word, despite the sweltering weather.
In the Yatsushiro area, where a chimney collapsed at a Nippon Paper Industries factory, 10 people were rescued, but eight others died, and one remained missing, according to the Kumamoto prefectural government disaster team.
