TOKYO — The Fukushima Dai-ichi nuclear plant could continue to release dangerous radiation into the air for several months, Japanese officials said Sunday, acknowledging their painstakingly slow progress in the battle to regain control of the badly damaged facility.

Goshi Hosono, a special adviser to Prime Minister Naoto Kan, first raised the specter of a months-long stabilization process during an interview with Fuji television. The government’s top spokesman, Chief Cabinet Secretary Yukio Edano, then confirmed the time frame at a news conference.

Edano told reporters that the government will continue to examine alternative emergency measures “to shorten that period,” but he conceded they “may not be feasible.”

The public disclosure that authorities were viewing the fight in a window of months, not days or weeks, illustrated the complex challenges and uncertain nature of the massive operation, now in its fourth week, to repair the crippled power plant. As if to underscore the likelihood that the emergency repair job will be replete with surprises, the Tokyo Electric Power Co. announced it had retrieved the bodies of two workers who had gone missing March 11.

Kazuhiko Kokubo, 24, and Yoshiki Terashima, 21, found Wednesday in the basement of the No. 4 reactor, were killed by the massive earthquake and tsunami that day, the company said, not by the subsequent release of dangerous radiation. They worked in the operation management division and were doing routine checks of the power plant when the quake struck, company officials.

The officials said they waited five days to publicly announce the deaths at the request of family members, who sought privacy.

“We feel extreme remorse about losing our young employees,” Tepco said in a company statement. “We promise that we will never repeat this tragedy.”

The announcement, coming a day after Tepco found irradiated water leaking into the sea from a crack in a storage pit at the No. 4 reactor, stoked fears about what other surprises lie in wait for emergency workers. Efforts to stem the leaking water, first by pouring concrete into the crack and then a water-absorbent polymer, have been unsuccessful, government officials said.

Asked about the ongoing problems, a spokesman for Japan’s nuclear regulatory agency insisted there has been “a degree of progress.”

“But there may be challenges we deal with for several weeks and others for several months and others that take even longer,” said Hidehiko Nishiyama, the deputy director general for the Nuclear and Industrial Safety Agency, which is monitoring Tepco.

The death toll from the March 11 disaster rose to 12,020, with another 15,512 still missing and 165,282 living in shelters, government officials said. An intensive three-day military operation to find bodies concluded Sunday after finding 77, according to news reports.

Tepco and the government have been criticized by outside experts, the media and the public for failing to disclose information in a timely, transparent manner. In response, the government has held several news conferences each day, including one for foreign reporters.

Armed with complex charts, government ministers from several agencies attempt to explain the incremental progress being made. But time and again, the small success stories have been overshadowed by more shocking revelations that steal the headlines and suggest the government has yet to establish the upper hand at the power plant.

One day last week, the International Atomic Energy Agency said it had found radiation in quantities it considered high enough to warrant evacuation outside the government’s 12-mile evacuation zone around the Dai-ichi plant. Another day, Tepco announced it had made a major error in reporting the radiation levels in water at the plant.

Deep skepticism has set in among reporters who pressed the government panel Sunday evening, asking why the discovery of the dead workers had not been announced last week and why top elected officials and Tepco executives were not appearing at the briefings.

“I will let the elected officials know of your concerns,” a government spokesman replied, without elaborating.