Environment minister Nobuteru Ishihara came under fire after saying money would be a decisive factor for local governments and residents being asked to accept plans to build storage facilities for radioactive waste.
The remarks were seen as insensitive to the tens of thousands of people who remain unable to return to homes around the crippled Fukushima nuclear power plant because of persistently high levels of radiation.
Fukushima Governor Yuhei Sato immediately hit back, saying: "It was extremely regrettable. The remarks rode roughshod over the feelings of residents who are longing for their hometowns."
Ishihara today told reporters "I sincerely apologise to those who were annoyed by my remarks."
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He said, however, that as the minister in charge of reconstruction, he would continue exploring proposals for waste-storage facilities, including details of compensation.
Central and local governments have been negotiating for months over the construction of "temporary" storage facilities for soil and other waste contaminated by fallout from the meltdowns at Fukushima following the 2011 tsunami.
Just three days after Japan's northeast was swamped by the huge tsunami, Ishihara senior caused outrage by saying the disaster -- which killed more than 18,000 people -- had been divine punishment for a nation obsessed by materialism.