Highly radioactive water overflowed barriers into Japan's Fukushima Daiichi nuclear power station after its operator Tepco underestimated how much rain would fall and failed to pump it out quickly enough.

Tepco has been battling to contain radioactive water at the nuclear complex, which suffered meltdowns and hydrogen explosions following a devastating earthquake and tsunami in March 2011.

Dealing with hundreds of tonnes of groundwater flowing through the wrecked nuclear station daily is a constant problem for the utility and for the government, casting doubt on the promises of Japan's prime minister, Shinzo Abe, that the Fukushima water "situation is under control".

After heavy rain on Sunday, water with high levels of radioactive strontium overflowed containment areas built around

some 1,000 tanks storing tonnes of radioactive water at the plant, Tepco said.

The radioactive water is a by-product of an improvised cooling system designed to keep the wrecked reactors under control in case of further disaster.

Tepco said it had planned to pump out the accumulating rainwater into empty tanks, check it for radioactivity, and if

it was uncontaminated, release into the sea. But the company was overwhelmed by the amount of rainwater.

"Our pumps could not keep up with the rainwater. As a result, it flowed over some containment areas," said Tepco

spokesman Yoshikazu Nagai.

The company had planned for 30mm to 40mm of rainfall on Sunday, but by late afternoon the rainfall already stood at about 100mm, he said.

The ongoing crisis at the Fukushima Daiichi plant, 220km north of Tokyo, highlights the immensity of the task of containing and controlling radioactive water and eventually decommissioning the plant, processes that are expected to take decades.

Tepco is seeking permission to restart its only remaining viable power station - Kashiwazaki Kariwa, the world's largest nuclear power facility, to cut high fuel costs and restore its finances.