TOKYO — The operator of Japan’s stricken Fukushima nuclear plant said Tuesday that it had found radioactive iodine at 7.5 million times the legal limit in a seawater sample taken near the facility, and government officials imposed a new health limit for radioactivity in fish.

The reading of iodine-131 was recorded Saturday, Tokyo Electric Power Co. said. Another sample taken Monday found the level to be 5 million times the legal limit. The Monday samples also were found to contain radioactive cesium at 1.1 million times the legal limit.

The exact source of the radiation was not immediately clear, though Tepco has said that highly contaminated water has been leaking from a pit near the No. 2 reactor. The utility initially believed that the leak was coming from a crack, but several attempts to seal the crack failed.

On Tuesday the company said the leak instead might be coming from a faulty joint where the pit meets a duct, allowing radioactive water to seep into a layer of gravel underneath. The utility said it would inject “”liquid glass”” into gravel in an effort to stop further leakage.

Meanwhile, Tepco continued releasing what it described as water contaminated with low levels of radiation into the sea to make room in on-site storage tanks for more highly contaminated water. In all, the company said it planned to release 11,500 tons of the water, but by Tuesday morning it had released less than 25 percent of that amount.

Although the government authorized the release of the 11,500 tons and has said that any radiation would be quickly diluted and dispersed in the ocean, fish with high readings of iodine are being found.

On Monday, officials detected more than 4,000 bequerels of iodine-131 per kilogram in a type of fish called a sand lance caught less than three miles offshore of the town of Kita-Ibaraki. The young fish also contained 447 bequerels of cesium-137, which is considered more problematic than iodine-131 because it has a much longer half-life.

On Tuesday chief cabinet secretary Yukio Edano said the government was imposing a standard of 2,000 bequerels of iodine per kilogram of fish, the same level it allows in vegetables. Previously, the government did not have a specific level for fish. Another haul of sand lance with 526 bequerels of cesium was detected Tuesday, in excess of the standard of 500 bequerels per kilogram.

Fishing of sand lances has been suspended. Local fishermen called on Tepco to halt the release of radioactive water into the sea and demanded that the company compensate them for their losses.

Fishing has been banned near the plant, and the vast majority of fishing activity in the region has been halted because of damage to boats and ports by the March 11 tsunami and earthquake. Still, some fishermen are out making catches, only to find few buyers because of fears about radiation.

It was unclear what Tepco might offer the fishermen, but the company did say Tuesday that it had offered “”condolence payments”” totaling 180 million yen ($2 million) to local residents who had to evacuate their homes because of radiation from the Fukushima plant. One town, however, refused the payment.

The company has yet to decide how it will compensate residents near the plant for damages, though financial analysts say the claims could be in the tens of billions of dollars. Tepco’s executive vice president Takashi Fujimoto said the company’s decision on damages hinges on how much of the burden the government will share.

Edano urged the company to accelerate its decisions on compensation.

For now the company has offered to give 20 million yen ($240,000) to each of 10 villages, towns and cities within 12 miles of the plant, Fujimoto said.

“”We hope they will find it of some use for now,”” he said.

Namie, a town of 20,600 located about 6 miles north of the plant, refused to take the money. Town official Kosei Negishi said that he and other government officials were working out of a makeshift office in Nihonmatsu city, elsewhere in Fukushima prefecture, and that they faced more pressing issues.

“”The coastal areas of Namie were hit hard by the earthquake and the tsunami but because of the radiation and the evacuation order we haven’t had a chance to conduct a search for the 200 people who are missing,”” Negishi said. “”Why would we use our resources to hand out less than 1,000 yen ($12) to every resident?””

Tokyo Electric Power’s Fujimoto acknowledged that there was a “”gap”” in the views of company and Namie officials.

Tepco’s shares dropped to an all-time low Tuesday, falling by the maximum daily trading limit — about 18 percent — to 362 yen, below the previous record low of 393 yen reached in December 1951. The company’s share price has lost 80 percent of its value — nearly 1.1 trillion yen — since the quake and tsunami, according to the Tokyo Stock Exchange.

“”We take the stock price decline very seriously,”” Fujimoto told reporters.

Fujimoto said the company’s annual earnings report, which was originally scheduled for April 28, would be postponed, but he declined to give any other details.