With the government inching closer to restarting the first nuclear reactors since last year's Fukushima Daiichi nuclear disaster, a new battleground between Japan's pro- and anti-nuclear camps is emerging: the annual shareholder meetings of the country's big power companies in June.

Japan's four biggest utilities hold their shareholder meetings on June 27. The meeting that's drawing a lot of attention these days is that of Kansai Electric Power Co., which relied on nuclear plants to supply around half of its electricity, and...