TOKYO — The Tokyo Electric Power Company, the utility trying to contain the crisis at the Fukushima Daiichi nuclear power plant, took a significant step forward on Friday when it began operating a huge filtration system that it hopes will ease the amount of contaminated water produced at its damaged reactors.

The filtering equipment, hastily cobbled together by several foreign and Japanese companies, is urgently needed because the storage facilities at the power plant are flooded with tens of thousands of tons of radioactive water and are expected to overflow as soon as next week if nothing is done.

If that occurs, Tokyo Electric, known as Tepco, would be forced to dump thousands of tons of even more tainted water into the ocean, and would probably bring down even more criticism on the embattled company and the government, which has been attacked for its handling of the crisis.

Hoping to avoid releasing any more contaminated water, Tepco in late April set out an ambitious nine-month road map for stabilizing conditions at its nuclear reactors. The plan includes setting up a sprawling water treatment plant that is expected to cost about $663 million. Built under the supervision of Toshiba and Hitachi, the filtration system is meant to sift out oil, and then cesium and other radioactive elements, before desalinating the remaining water.