The magnitude 7.1 earthquake hit Japan's southern main island of Kyushu on Tuesday.
Officials said 34 deaths had been confirmed as related to the disaster, with one more death still under investigation.
Authorities said more than 80 people had been injured, five of them seriously.
Searchers continued to work in the Kumamoto area on Friday, including at the site of the collapsed mall.
Residents in southwestern Japan have camped in classrooms and vehicles, stocked up on water and tried to get back to normal, two days after a powerful earthquake killed at least 25 people.
Time was running out to find survivors on Friday, as rescuers continued to work in the Kumamoto area on Japan's southern main island of Kyushu, where the magnitude 7.1 earthquake struck on Tuesday. The number of people missing was unclear.
Of the deaths given in the latest tally, 25 have been confirmed as related to the disaster, but there were nine more deaths under investigation as likely to be connected, the Kumamoto prefectural government said. The quake left at least 86 people injured, five of them seriously, it said.
Thousands of people spent another night at evacuation centres set up throughout the area at schools and other big spaces. Some homes were still without water or electricity, while others were simply afraid to go back.
More than 3500 homes were still without electricity and more than 9000 people were staying in around 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 heatstroke alert for the Kumamoto area, with temperatures rising above 33C on Friday.
Risks of heatstroke are a major concern among officials.
Yutaka Kobayashi, a doctor dispatched from central Japan's Aichi prefecture, said he was touring evacuation centres on Thursday to assess the condition of evacuees, especially elderly people and those with injuries as they cope with a harsh environment.
"We have to make sure elderly people are not developing heatstrokes or dehydration," he said in Hikawa.
While the town parking lot was nearly packed the first night, some residents have moved to three public schools where air-conditioning is running, Hikawa officials said.
A town official, Yuzuru Tamura, said they are starting to run out of emergency food supply, such as canned bread and instant rice.
Searchers continued to work in the Kumamoto area on Friday, including at the site of the collapsed Aeon Mall shopping centre in the town of Kashima, where some of the most serious damage was recorded. The complex was bustling with thousands of people when the quake happened.
The company said about 3000 shoppers were evacuated to a parking lot before an explosion happened in another part of the mall, where some staff remained working. The mall's second floor collapsed, trapping people.
Footage provided by the Japanese government and military showed rescue workers drilling through the collapsed parts of the building in an attempt to get to anyone who may still be trapped inside.
Prime Minister Sanae Takaichi told reporters the central government will take a lead role in co-ordinating the various rescue efforts. Restoring electricity, gas and water to stricken areas, while providing a supply of fresh water is key.
"The needs on the ground are constantly changing. To put to rest the people's feelings of uncertainty, we will do all that needs to be done," she said.