TOKYO — Tens of thousands of gallons of radioactive water leaked from a large underground storage pool at Japan’s crippled nuclear plant, and thousands more gallons could seep out before the faulty pool can be emptied, the plant’s operator said Saturday.

About 120 tons, or almost 32,000 gallons, of highly contaminated water appeared to have breached the inner protective lining of the pool at the Fukushima Daiichi plant, said the operator, Tokyo Electric Power Company. It was unclear how much of the water had made it through two additional layers of lining to reach soil, but radiation levels outside the pool have risen, a sign that some water is getting out, said the company, known as Tepco.

The leak highlights the daunting challenge of what to do with the huge amounts of contaminated water created by makeshift cooling systems at the plant, after a huge earthquake and tsunami knocked out its regular cooling systems two years ago in the worst nuclear accident since Chernobyl. Since then, Tepco has essentially been pouring water onto the damaged reactor cores and storage ponds to keep them from overheating.

As it is used for cooling, the water becomes so contaminated that it must be safely stored at the plant. Tepco said it was already storing more than a quarter-million tons of radioactive water in hundreds of large silver or blue tanks that seem to fill every available space at the plant, or in underground pools like the leaking one. With the decommissioning of the Fukushima plant likely to take decades, Tepco has said it expects the amount of radioactive water to keep growing, and possibly more than double within three years. The company has said it is building more storage space and new filtering facilities to clean the water.