TOKYO—Japan faced new setbacks in its struggle to tame a quake-ravaged nuclear complex as a fresh fire broke out there early Wednesday, workers were temporarily moved to safer locations, and new threats emerged in previously unaffected parts of the plant.

Radiation levels began rising sharply around 10 a.m. local time, according to a government spokesman, forcing outdoor workers at the power plant to move indoors, away from the most radioactive areas. But by 11:30 a.m. the workers were back on the job, the government's nuclear...