Japanese authorities on Monday urged millions to evacuate their homes after heavy rains unleashed floods and landslides in the country's southwest, leaving several residents missing.

Television footage from various communities in Kumamoto prefecture showed houses, stores and vehicles submerged in about a metre of water.

Surging rivers swept away vehicles and damaged roads.

In six hours to early Monday, more than 37 centimetres of rain fell in Kumamoto prefecture's hardest-hit Tamana city, a record for the area, according to the Japan Meteorological Agency.

Evacuation advisories and warnings were issued to more than three million residents in the southwestern regions, according to the Fire and Disaster Management Agency.

Some 384,000 residents, mostly in Kumamoto, faced Japan's most serious evacuation warning, it said.

A father in Kosa town in Kumamoto went missing early on Monday after a landslide hit near his house while he stood outside his vehicle, a town official said.

His wife and their two children were safe inside the car, the official added.

In Misato town, also in Kumamoto, rescuers were trying to reach an elderly man trapped inside his house after it was struck by a landslide, the town's duty official said.

And two people in Fukuoka city reportedly were swept away in a surging river on Sunday and remained missing, Japan's broadcaster NHK said. (AFP)