The death toll in the worst typhoon to hit Japan for decades climbed to 58 on Tuesday as rescuers slogged through mud and debris in an increasingly grim search for the missing, and as thousands of homes remained without power or water.

Fifteen people remain missing nearly three days after Typhoon Hagibis smashed into central and eastern Japan, NHK national broadcaster said. More than 200 people were injured in the storm, whose name means "speed" in the Tagalog language.

About 138,000 households were without water while 24,000 lacked electricity, well down on the hundreds of thousands initially left without power but cause for concern in northern areas where temperatures are falling.

The highest toll was in Fukushima prefecture north of Tokyo, where levees burst in at least 14 places along the Abukuma River, which meanders through a number of cities in the largely agricultural prefecture.

At least 18 people died in Fukushima, including a mother and her child who were caught in flood waters. The woman's son, who was also with her in the flood, remains missing.

Survivors described how water rose rapidly to chest height in about an hour and mainly at night, making it hard to escape to higher ground. Many of the dead in Fukushima were elderly, NHK said.

"I couldn't believe it, the water came up so fast," one man in Fukushima told NHK.

Major highways remained closed in Koriyama city in Fukushima prefecture as people began commuting to their first day of work after the storm and a long weekend. Children in uniforms walked to school and while some stores remained closed, others were open.

Around the nation, manufacturers took stock. Electronics maker Panasonic Corp said flooding had damaged its plant in a large industrial park in Koriyama.

Automakers Nissan, Honda and Subaru said there was no major damage to their factories, while Toyota said all its plants were operating normally.

Prime Minister Shinzo Abe warned that the economic impact could be prolonged.

"The national government will continue to do everything possible so that the victims of this disaster can return to their normal lives as soon as possible," Abe told a parliamentary committee.

Finance Minister Taro Aso said there was 500 billion yen ($4.6 billion) in reserves for disaster recovery and more money would be considered if needed.

Thousands of police, fire officials and military personnel continued to search for people who may have been cut off by floodwaters and landslides, with hope diminishing that the missing would be found alive.

Though the threat of rain is expected to diminish on Tuesday, temperatures are likely to drop in many areas later this week, in some cases to unseasonably low levels, NHK said.

Four of Japan's major refiners said there was no impact on their refinery operations from the storm. ($1 = 108.3300 yen)