More than 70 people have died and dozens are missing as torrential rain hammered parts of Japan for a third day on Sunday, with the prime minister, Shinzo Abe warning that rescue workers faced a “race against time”.

Continued rainfall prompted disaster warnings on the south-western main islands of Kyushu and Shikoku, as local media reported the death toll had risen overnight to 76, with 92 people missing.

At one point, evacuation orders or advisories were issued for 4.72 million people, while around 48,000 members of the self-defence forces, police and firefighters were mobilised to search for trapped or injured people or to recover bodies.

The government’s top spokesman, Yoshihide Suga, said most of the missing people were in the southern part of Hiroshima prefecture but that their exact whereabouts were unknown.

The heaviest rainfall Japan has seen in decades has caused widespread flooding and landslides, with reports of cars being swept away by floodwater and people taking refuge on the roofs of their inundated homes.