An unusual bureaucratic battle is under way inside the U.S. government over which agency will finance and supervise American participation in the Soviet medical and environmental follow-up to the Chernobyl nuclear power plant accident, according to Reagan administration officials.

Those vying for the role include the Department of Energy, the National Institutes of Health and the National Academy of Sciences, each of which has a different motive in wanting to study the most extensive radiation exposure in 41 years.

More is involved than running a few long-term studies. Relatively little data exists about the effects of radiation on large populations because broad-scale exposure to relatively large doses of the magnitude of Chernobyl took place only after the United States dropped the first atomic bombs at Hiroshima and Nagasaki in August 1945.

"This is a unique opportunity to gather data that would be helpful to all mankind," one official said. "Up to 100,000 people were exposed to a variety of radiation levels, and to track their health effects over a long term would be invaluable."

Complicating the U.S. government's situation, however, is the fact that an agreement for a joint U.S.-Soviet study of the medical and biological consequences of the accident already exists between Moscow and a private U.S. citizen.

On June 6, Dr. Robert Gale, the Los Angeles surgeon who performed bone marrow transplants in Moscow on victims of the accident, negotiated and signed the document on the U.S. side, and Dr. Andrei Vorobyov, a corresponding member of the U.S.S.R. Academy of Medical Sciences, signed for the Soviets.

The paper does not say who would organize the study, but Gale said in a recent interview that "the Soviets made clear they were interested in a scientific, collegial relationship and not a government one. I think that is appropriate."

Gale believes, however, that the postaccident study, which would log the cases of up to 130,000 persons in computer banks and provide for regular, documented medical examinations over a 30-year period, should be organized quickly "because a lot of data is already disappearing."

The Soviets say they have already begun the process. In a radio interview earlier this month, Leonid Ilin, a member of the Soviet academy and the U.S.S.R. representative on the United Nations' scientific committee on the effects of atomic radiation, said each of the roughly 100,000 people evacuated from inside the 30-kilometer area around Chernobyl was examined for possible radiation, including blood and thyroid gland tests specifically looking for radioactive iodine.

The Associated Press reported Monday that workers have completed a concrete foundation under the ruined No. 4 reactor at the Chernobyl nuclear power station, finishing the project three days ahead of schedule, according to a television broadcast.

Officials have said they plan to entomb the reactor in a concrete "coffin" to seal off radiation for the hundreds of years needed for the fuel inside to decay.

A Radio Moscow report suggested the coffin around the ruins of the reactor, ripped open by an explosion April 26, will now be started. No estimates were given for how long the project will take.

Gale said he has been in touch with the State Department. Officials there said they are aware they will have to deal with Gale, but one government official added, "We are uncertain about Gale's agreement . . . and have not reached any conclusion about it."

Before and after Gale's agreement was announced, officials from the interested U.S. agencies made direct proposals to the Soviets through various channels or the State Department. So far none has received a positive response.

The National Institutes of Health is interested in medical aspects of the disaster. For example, it has a July 20 meeting planned in Moscow to discuss reinvigorating a 1972 agreement for study of cancer and the environment.

The reason for the Department of Energy's interest, given the U.S. reactor safety program, is obvious, but that department's biomedical group also has supervised the medical follow-up for 32 years on natives of the Marshall Islands who were exposed to fallout from a 1954 U.S. hydrogen bomb test.

The National Academy of Sciences has supervised the U.S. portion of the Hiroshima-Nagasaki victims studies that began in 1945. An official there said the NAS president, Dr. Frank Press, had sent a cable "several weeks ago" to Yevgeney Velikhov, vice president of the U.S.S.R. Academy of Sciences and a personal friend. Press proposed to work out a follow-up program with a series of U.S.-Soviet workshops or conferences that would be held under an existing agreement between the two academies. Velikhov, who has been directing the scientific side of the Chernobyl cleanup, has yet to respond, the NAS official said.

Gale is planning to join NIH officials at their July 20 meeting and said he hoped the agenda could be expanded so he could offer "a U.S. plan for the Chernobyl follow-up studies for the Soviets to study and respond."

Currently, State Department officials are trying to broker a unified U.S. government position, and a spokesman said that some agreement could be reached next week.

The rivalry, however, is intense. One NAS official pointed out that "Gale, as a surgeon, had no experience in epidemiology," the statistical study of the incidence and distribution of disease within a society, which would be a major element of the follow-up.

"The Russians seized on Gale as a contact to embarrass the U.S.," another official said. "It is more appropriate that U.S. funds go through some official group."

A Soviet diplomat smiled and shook his head last week when asked whether Moscow would accept a DOE presence in the Chernobyl follow-up. He said that DOE not only built U.S. nuclear weapons, but also its officials actively opposed Washington's joining Soviet leader Mikhail Gorbachev's moratorium on underground nuclear tests.

One U.S. official said of the skirmish, "It's confusing, but it's not totally true that the left hand doesn't know what the right hand is doing. It's a turf battle and it's a little premature for a solution yet."