The two control room operators are being tested further and don’t have immediate health problems, Tokyo Electric Power Co. said Monday. If confirmed, they would be the first men to reach the government-set limit.

TEPCO has been criticized for not fully disclosing the extent of radiation exposures by the plant workers or their working conditions, raising suspicion they may not be closely monitored or informed of potential risks.

The conventional limit of 100 millisieverts was raised to 250 millisieverts for male workers — equivalent of more than 30 CT scans — to confront the problems the March 11 earthquake and tsunami set off at the Fukushima Dai-ichi plant.

Thirty plant workers have exceeded 100 millisieverts, according to TEPCO.

The two men were responsible for central control rooms at Unit 3 and 4 reactors when the disasters knocked out the plant’s power and cooling functions.

“The possibility (of the two men) exceeding the limit underscored the severity of working environment at the plant,” said Goshi Hosono, director of the government’s nuclear crisis taskforce, urging TEPCO to conduct internal exposure tests for all plant workers as quickly possible to assess the extent of whole body exposures.

Experts also urged that other workers be checked as soon as possible because those who were outside the control rooms could have been exposed to higher levels of radiation.

The two men are no longer working at the plant. They had external exposures of 74 millisieverts and 89 millisieverts, but high iodine levels in their thyroid glands detected in April and May could push their total exposure beyond 250 millisieverts, TEPCO spokesman Junichi Matsumoto said.

The two men were believed to have taken a preventive iodine pill and officials are checking whether one pill was enough protection, Matsumoto said. The pills can prevent thyroid cancer, one of the more common illnesses caused by high radiation exposure, but must be taken quickly.

Radiologists who have examined the two men said Monday they need not be hospitalized because they have no acute symptoms that require treatment.

External contact with radioactive particles in the air and water can be washed off. Internal exposure is from inhalation or swallowing.

Nuclear and Industrial Safety Agency spokesman Hidehiko Nishiyama said a failure to observe the exposure limit is subject to punishment such as suspension of license or suspension. He fell short of saying whether TEPCO would face an unprecedented penalty.

Authorities also reported a mishap occurred over the weekend. A heat removal pump failed at Unit 5, which came to a stable, cold shutdown after the tsunami. But the failure allowed the core water to heat nearly to boiling before the pump was replaced and cooling resumed Sunday afternoon. The temperature has since declined to 57.4 Celsius (135 F) — around the level before the problem.

Also Monday, Typhoon Songda caused heavy rains around the plant and other areas of the coast devastated by the tsunami. TEPCO said the rains caused no damage to buildings, but contaminated water that had been pooling inside the plant swelled further. No leaks into the sea were detected, however.

A Fuji Television Network poll released Monday showed more than 80 percent of Japanese voters do not trust government information about the country’s nuclear crisis. About the same percentage of respondents said TEPCO is dealing with the crisis poorly.

The weekend national poll of 1,000 eligible voters on the phone gave no margin of error, but a poll of that size would normally have a margin of error of about 4 percentage points.