Okayama Prefecture had 22 residents killed, while Kyoto Prefecture had four fatalities and Yamaguchi Prefecture three.
The heavy rainfall has been attributed to the remnants of a typhoon feeding into a seasonal rainy front.
Rescue and recovery effort continues, according to authorities.
And with many people stuck in modestly equipped shelters with few possessions, or living in damaged homes with no running water or electricity, the rising temperatures posed a new problem, authorities said.
Some 276,000 households now lack water supply, Kyodo news agency reported.
Electronics maker Panasonic said one plant in Okayama, western Japan, could not be reached due to road closures, although it had been closed for the weekend.
Carmakers including Mazda and Daihatsu suspended operations at several plants last Saturday.
Japan on Thursday ordered the evacuation of thousands of residents from the outskirts of its ancient capital of Kyoto after "historic" rains battered its western region, killing a man, with yet more rain forecast.
Flooding and storms in western and central Japan killed at least two people, local reports said.
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Japanese public broadcaster NHK reported about 364 millimeters (14.3 inches) of rain fell between 5 a.m. and 7 a.m.in the city of Uwajima - approximately 1.5 times the average monthly rainfall for July. Rivers overflowed, turning towns into lakes, leaving dozens of people stranded on rooftops. Some 40 helicopters were out on rescue missions.
Evacuation orders or advisories were issued to more than 910,000 people, it said. Hiroshima prefecture has been severely affected by rains.
Rescue workers and troops have been struggling in the mud and water to save lives. "There are still many people who have been unaccounted for".
The heavy rains triggered massive landslides in some areas: "There have been massive flooding and landslides", government spokesman Yoshihide Suga told a news conference. Critical infrastructure has been hit, including railway tracks.
Japan's government set up an emergency management centre at the prime minister's office and some 54,000 rescuers from the military, police and fire departments were dispatched across a wide swath of southwestern and western Japan.
Okayama prefecture, south of Hiroshima, said in a statement that five people had died, seven were missing and 11 were injured, at least one of them seriously.
The Japan Meteorological Agency (JMA) said one area in Kochi prefecture had recorded 263mm of rain in three hours, the highest since such records started in 1976.