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At least 13 people were also missing after a month's worth of rain fell overnight, loosening slopes already saturated by heavy rain over the past few weeks.
"There was rain and thunder all night, beating down so hard I was scared to go outside," a resident told Fuji TV. "Great big drops. I've never seen anything like this."
Helicopters clattered overhead as rescue workers searched through mud and piles of stones in residential areas about 5 km (3 miles) from the centre of the city.
Among those dug out of the debris was a two-year-old boy who was not breathing but it was not clear if he had been killed, media reported.
With land in short supply in many parts of Japan, cities often expand into mountainous areas, leaving such development vulnerable to landslides.
About 240 mm (9 inches) of rain fell in the area in the 24 hours up to Wednesday morning, record-breaking levels equivalent to a month's worth of rain in a usual August, Japan's Meteorological Agency said.
Asphalt roads crumbled under the force of one landslide, while streams of mud cut swathes through neighbourhoods, turning houses into piles of twisted wreckage.
Prime Minister Shinzo Abe cut short his summer vacation to head back to Tokyo as authorities asked for help from the military for rescue efforts.