Japanese authorities told tens of thousands of people to evacuate the quake-hit region of Ishikawa on Saturday as "unprecedented" rains triggered floods and landslides.
A dozen rivers in the region, on the west coast of central Japan, had burst their banks by 11:00 am (0200 GMT), land ministry official Masaru Kojima said.
Three people were missing in Ishikawa, public broadcaster NHK reported, two of them carried away by strong river currents.
At least one person was missing further north in Wajima, and rescue workers were trying to confirm a report of another person missing, a local official told AFP.
Many buildings were inundated, with landslides blocking some roadways, the Ishikawa government said in a statement.
The cities of Wajima and Suzu, as well as Noto town, ordered about 44,700 residents to evacuate, officials said.
The Japan Meteorological Agency (JMA) said it issued its highest-level warning for Ishikawa, cautioning of a "life-threatening situation".
More than 120 millimetres (4.7 inches) of rainfall per hour was recorded in Wajima in the morning, the heaviest rain since comparative data became available in 1929.
Footage on NHK showed an entire street submerged in Wajima.
Prime Minister Fumio Kishida instructed the government "to do its best in disaster management with saving people's lives as the first priority", top government spokesman Yoshimasa Hayashi told reporters.
Self-Defense Forces personnel have been sent to the Ishikawa region to join rescue workers, he said.
At least one house was hit by a landslide, the Fire and Disaster Management Agency said, without giving further details.
Another 16,700 residents in Niigata and Yamagata prefectures north of Ishikawa were also told to evacuate, the agency said.
Some 6,600 households in the region were without electricity by Saturday afternoon and communication services were cut for some people, operators said.
Wajima and Suzu, in central Japan's Noto peninsula, were among the areas hardest hit by a huge New Year's Day earthquake that killed at least 236 people.