Nearly a million more people were advised to leave their homes after the country's weather agency raised the alert to its highest level for parts of northern Kyushu.
The emergency warning is issued "if there is a significant likelihood of catastrophes".
Officials confirmed two deaths, one in western Saga prefecture where a man was found in a car that had been swept away. A second man died in Fukuoka as he tried to escape from a car trapped in rising floodwaters.
Government spokesman Yoshihide Suga said a third person, in Saga, was in a state of "cardiorespiratory arrest" -- a term usually used by Japanese officials to indicate a person's death before it is officially confirmed by a doctor.
"There are many reports of damage in different areas due to flooding of rivers, landslides, and submerged houses, and there is a possibility of serious damage occurring in the coming hours," Suga added.
Evacuation orders and advisories issued by local authorities are not mandatory, although officials urge residents to heed them.
The fire and disaster management agency said it had already received multiple reports of flooded houses in Saga and Nagasaki prefectures.
"We are seeing unprecedented levels of heavy rains in cities where we issued special warnings," a spokesman for the Japan Meteorological Agency told reporters.
"It is a situation where you should do your best to protect your lives," weather agency official Yasushi Kajiwara said.
He also urged those living in areas currently under evacuation advisories to act quickly.
"Please don't wait," he said.
The JMA's emergency warnings affect areas in Saga, Fukuoka and Nagasaki, where the severe weather has also disrupted transport, forcing the suspension of some train services and some road closures.
Television footage showed rivers swollen by the rain and parked cars sitting in muddy brown water nearly up to the vehicles' roofs.
Small landslides have already been reported.
At a station in Saga, stranded passengers sat on benches with water around their ankles.
Japanese authorities regularly urge people to take evacuation orders seriously, particularly after disastrous heavy rains last summer in Japan's west killed more than 200 people.
Many of the deaths were blamed on the fact that evacuation orders were issued too late and some people failed to follow them. Entire neighbourhoods were buried beneath landslides or submerged in floodwaters during the disasters.