Tokyo Electric Power Co. said some of the water is seeping over or around an underground barrier that was created by injecting chemicals into the soil that solidified into a wall.
TEPCO spokesman Yoshikazu Nagai said the company was slow to deal the leaks because it was focusing on cooling the damaged reactors, which posed greater risks.
The water has built up over the last month since the company began creating the chemical barrier to stop leaks. Radiation spikes in water samples were detected in May, prompting the creation of the walls.
Three reactors at the wrecked Fukushima Dai-ichi plant suffered meltdowns after the massive earthquake and tsunami in March 2011. Power and cooling systems were destroyed in the disaster.
The plant is still running on makeshift equipment and has been plagued with blackouts and leaks from underground tanks.
The Associated Press contributed to this report.