TOKYO—Officials at Japan's Fukushima Daiichi nuclear-power complex said late Thursday they had found radioactive groundwater just outside a troubled reactor building, capping a day of uncertainty that saw Japan's prime minister question the country's pursuit of nuclear power.

In a brief statement, Tokyo Electric Power Co., the plant's operator, said a test of groundwater conducted the previous day at the site revealed radioactive iodine-131—a common isotope found there since it was damaged by the earthquake and tsunami on...