He added: "Please do not hesitate to let us know if Singapore can be of assistance to the ongoing relief efforts".
In western Okayama prefecture, around 200 people including children and elderly people were trapped in a hospital after a river burst its banks and flooded the surrounding area.
Footage showed a massive rescue operation, with some 1,850 people isolated in the city, according to public broadcaster NHK.
The disaster is the deadliest rain-related crisis in Japan since 2014, when at least 74 people were killed in landslides caused by torrential downpours in the Hiroshima region. 'The rescue teams are doing their utmost'.
Local government officials said pumping trucks were being deployed to help restore access to some of the worst-hit areas.
"We urge residents to remain cautious about possible landslides", a weather agency official told AFP.
In Hiroshima prefecture, rescue workers found the body of a three-year-old girl whose home had been hit by a landslide.
"I went to my father's family home but it was hopeless", one man said.
"I can't reach her phone", he told AFP, sitting across from a house that had been ripped apart and tossed on its side by a huge landslide.
Government response: The Japanese government set up an emergency management center at the prime minister's office and has dispatched approximately 54,000 military, police and firefighters to carry out the rescue missions and provide disaster relief.
Okayama prefecture, south of Hiroshima, said in a statement that five people had died, seven were missing and 11 were injured, at least one of them seriously.
Major manufacturers in the area around Hiroshima and Okayama, such as Panasonic, Mazda, and Mitsubishi Heavy Industries, have shuttered factories.
Rain tapered off across the western region battered by last week's downpour, revealing blue skies and scorching sun forecast to push temperatures above 30 degrees Celsius (86°F), fuelling fears of heatstroke in areas cut off from power or water. Rivers overflowed, turning towns into lakes, leaving dozens of people stranded on rooftops.
"I've lived here for 40 years. I have never seen anything like this", he said, standing in shock before the house where he and his wife raised their three daughters, all now adults.
The death toll from unprecedented rainfall in Japan has risen to at least 76, as widespread flooding forces millions from their homes.
While evacuation notices are no longer in effect, two million people are still being advised to keep away from their homes. The rains have triggered mudslides and landslides that have killed people who got caught outside.
And the death toll was expected to rise further, with local media reporting almost 90 people killed and over 50 others unaccounted for. Dozens more remained missing.