The overall death toll from the rains in Japan rose to at least 66 on Sunday from 49 overnight after floodwaters forced several million people from their homes, media reports and the Fire and Disaster Management Agency said.
In Kurashiki, 2,310 people have been rescued by authorities and the search still continues.
Almost 50,000 members of the military, police and firefighting services were taking part in searches for people trapped, wounded or dead as a result of the floods, reported the Japan Times.
Such warnings are issued in anticipation of the sort of extreme conditions that occur just once or twice in 50 years, Kyodo News reported.
"There are still many people missing and others in need of help", he told reporters.
Several major manufacturers, including carmakers Daihatsu and Mitsubishi, suspended operations at plants in the affected areas.
Millions of people were advised to evacuate their homes.
"This is heavy rain at a level we've never experienced", a JMA official said as the agency issued warnings in Okayama, Hiroshima, Tottori, Fukuoka, Saga, Nagasaki, Hyogo and Kyoto prefectures.
In the town of Mihara, in the south of the Hiroshima region, a let-up in rain laid bare the devastation wrought by the downpours. "There are still many people who have been unaccounted for".
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.
Japanese Prime Minister Shinzo Abe told his cabinet on Saturday to take "every measure to prevent the disaster from worsening by taking advance actions".
Another 58 were missing, NHK said, and more rain was set to hit some areas for at least another day.
Japanese government spokesman Yoshihide Suga said the whereabouts of 92 people is unknown, mostly in the southern area of Hiroshima prefecture.
Rescue operations by Self-Defense Forces personnel and others were continuing in disaster-hit areas early Monday, as Japan's weather agency warned the public of the continuing danger of landslides and flooding.
The toll has risen steadily since then, and the conditions have made rescue operations hard, with some desperate citizens taking to Twitter to call for help.
The death toll is higher than that seen in 2014, when more than 70 people died in landslides caused by torrential rain in Hiroshima.
The Japan Meteorological Agency said three hours of rainfall in one area in Kochi prefecture reached an accumulated 26.3 centimetres, the highest since such records started in 1976.