TOKYO—Japan is preparing to start up a massive nuclear-fuel reprocessing plant over the objections of the Obama administration, which fears the move may stoke a broader race for nuclear technologies and even weapons in North Asia and the Middle East.

The Rokkasho reprocessing facility, based in Japan's northern Aomori prefecture, is capable of producing nine tons of weapons-usable plutonium annually, said Japanese officials and nuclear-industry experts, enough to build as many as 2,000 bombs, although Japanese officials say...