TOKYO—One of the images symbolizing Japan's postwar economic boom is a blue-and-white bullet train streaking past Mount Fuji on the world's first high-speed railway line, which went into service on the eve of the 1964 Tokyo Olympics.

Half a century later, Prime Minister Shinzo Abe wants to use another leap in train technology to demonstrate that even after two decades of economic decline, Japan can still think big. The company that operates the original bullet train, linking Tokyo to Osaka, intends to build a new line that...