Yukio Edano, the chief cabinet secretary, said early Tuesday that the makeup of the plutonium in the soil suggested that traces could be escaping the reactors. Together with the highly radioactive water, he said, this could be more evidence that fuel rods inside some of the reactors may be damaged. “There is a high possibility that there has been a slight melting of the fuel rods,” he said.

A full meltdown of the fuel rods would be catastrophic, releasing great amounts of radiation.

The trick now, Mr. Edano said, is to keep pumping enough water to ensure that these fuel rods do not overheat, at the same time trying to minimize the overflow of contaminated water.

Shares of Tokyo Electric were offered at 566 yen, or $6.93, early Tuesday on the Tokyo Stock Exchange after plunging 18 percent on Monday to 696 yen, or $8.52, the lowest in more than 30 years. The newspaper Yomiuri on Tuesday cited anonymous sources as saying the government would temporarily take a majority stake in the company, effectively nationalizing it, to help it pay for the enormous damages from the accident.

But Mr. Edano denied the report, saying, “We’re not currently considering that.”

All the reported readings are within the safe range of plutonium levels in sediment and soil given by the United States Agency for Toxic Substances and Disease Registry. But Tokyo Electric said the highest reading was more than three times the level found in Japan compared with the average over the last 20 years. American nuclear experts expressed confusion on Monday about the company’s latest report that one form of plutonium was found at elevated levels at the Fukushima plant while other forms were not, and suggested it could be a measurement error.