Most of the deaths have occurred in Hiroshima prefecture, which has been hit by torrential rain since Thursday.
According to the count by The Asahi Shimbun, of the 62 people who died, 27 were in Hiroshima Prefecture, 18 in Ehime Prefecture, eight in Okayama Prefecture, three in Yamaguchi Prefecture, two in Fukuoka Prefecture, and one each in Shiga, Kyoto, Hyogo and Kochi prefectures. Majority were rescued by boats or helicopters.
Kyoto officials said it was working to control flooding at several dams and identified one fatality as a 52-year-old woman.
A picture shows cars trapped in the mud after floods in Saka, Hiroshima prefecture. Almost 50,000 members of the military, police and firefighting services were taking part in searches for people trapped, wounded or dead as a result of the floods, reported the Japan Times.
Japan Ground Self-Defence Force rescues residents from a flooded area in Kurashiki, Okayama prefecture, on July 7, 2018 after record rainsfall hit western Japan.
The heavy rains triggered massive landslides in some areas: "There have been massive flooding and landslides", government spokesman Yoshihide Suga told a news conference.
In western Okayama prefecture, rescue operations were underway to evacuate several hundred people including children and the elderly from a hospital, some by helicopter.
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On Saturday, Abe warned at an emergency government meeting that "the situation is extremely serious" and ordered his government to "make an all-out effort" to rescue those affected. However, around 80 people remained at the hospital as of Sunday evening, according to the NHK public broadcaster.
Over 50,000 rescue workers, police and military personnel have been mobilised to respond to the disaster, which has left entire villages submerged by flooding, with just the top of traffic lights visible above the rising waters.
Okayama prefecture said three people had died, six others were missing and seven were injured, one of them seriously. Military paddle boats were also being used to take people to dry land. Evacuation orders had been issued to more than 360,000 people, the prefecture said in a statement.
A nursing home is reportedly flooded in Kurashiki City, although further details are still unknown.
A resident struggles to cross a collapsed road destroyed by heavy rain in Higashihiroshima in Hiroshima Prefecture on Saturday.
NHK TV said water had reached as high as 16ft in the worst-hit areas. Also in Ehime, two elementary schoolgirls and their mother who got sucked into a mudslide were pulled out but could not be revived.
Information about the people at the municipal shelters is still sparse, while social media buzzes with photos and video of the disaster-stricken country.