One 63-year-old woman was killed after her house was crushed by a landslide and another when her car was swept away. At least 27 people were injured, eight seriously.
Two eight-year-old children were believed to be among the missing, NHK national television said.
Helicopters crisscrossed skies over the largely rural city of Osaki, some 220 miles north of Tokyo, where the brown waters of the Shibui river inundated rice fields and houses as rescuers in rubber boats ferried people to safety.
Some parts of Japan had received more than twice the usual September amount of rain in 48 hours by noon on Thursday, sparking some of the worst flooding in more than 60 years.
Japan has put heavy emphasis on disaster prevention since a 2011 earthquake and tsunami killed nearly 20,000 people, and authorities are keen to avoid the kind of criticism they faced then for what was seen as a sluggish response.
The government set up an emergency center, and Prime Minister Shinzo Abe told a meeting of ministers that the "unprecedented" rain had created an emergency.
"The central government, police, fire officials and military are all working as one," chief cabinet secretary Yoshihide Suga told a news conference. "We are doing everything in our power to rescue those in need as soon as possible."
Some 51 helicopters and nearly 6,000 rescuers worked into the night on Thursday to pluck stranded people from houses as floodwaters raged below. More than 100 were temporarily trapped on the second floor of a shopping center in Joso.
Toyota Motor Corp said it had suspended production at three plants in northeastern Japan on Friday morning but that there had been no damage at any of the facilities.
Reuters
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