The State Department has issued a three-page statement defending its role in the Charles Horman case, the subject of the new Costa-Gavras film, "Missing."

The film, starring Jack Lemmon and Sissy Spacek, is based on the story of Charles Horman, an American free-lance journalist who was killed in Chile in 1973 during the overthrow of the Salvador Allende government. His father, Edmund Horman, traveled to Chile in search of his missing son, and there -- according to him and the film version -- encountered uncooperative and unfriendly American Foreign Service officers who offered little help in the search. The film, which opens here Friday, implies U.S. complicity in Horman's death and also possible U.S. involvement in the right-wing coup.

The statement, released Tuesday, reads: "The Department of State undertook intensive and comprehensive efforts to locate Charles Horman from the moment it was learned that he was missing, to assist his relatives in their efforts to locate him and also to learn the circumstances of his disappearance and death."

The statement says officials investigated and provided documents on the Horman case to the family, which filed suit against the secretary of state and other State Department officials for damages arising from Charles Horman's death.

"The results of these investigations," says the statement, "were summarized by Secretary of State [Edmund] Muskie, who testified by affidavit in the Horman case that the State Department officials who investigated and considered this matter have found no evidence of involvement by any United States Government personnel in the disappearance and death of Charles Horman."

Reached in New York, Costa-Gavras, a Greek director who lives in Paris, responded with surprise to the statement. "I think they overreacted," said Costa-Gavras, whose other films include "Z," "State of Siege" and "The Confession." "If with the big problems of the world, they take this much time [to react to a movie], that is too much. They should need a lot of brains working."

Reaction to the film has been strong in Washington.

Said State Department lawyer Judd Kessler, one of the defendants named in the Horman suit: "I think it's a political piece of merchandise and I think it's a big, fat lie."

Edmund Horman, reached in New York, said, "There is nothing in that movie that wasn't based on absolute fact."

Charles Whitehouse, president of the American Foreign Service Association, said he was working on a statement from his organization that read in draft form, "It is especially unfortunate in this particular situation that officers who worked diligently under dangerous conditions and who made special efforts on behalf of American citizens in Chile at that time were made defendants in the Horman civil suit, denigrated in the Hauser book ["The Execution of Charles Horman," by Thomas Hauser, on which the movie is based], and misrepresented in the film."

The issuing of a statement was not without precedent. When "Midnight Express," the story of an American drug smuggler imprisoned in Turkey, opened, the State Department issued a statement to answer many questions that arose. In the case of "Missing," a film that has not opened here but has been previewed at various screenings this week, the State Department anticipated questions.

"Various articles about the film caught our eye," said State Department press officer Anita Stockman. "We brought it to the attention of various officers. Because of that, they thought, 'Maybe we ought to have information prepared in case there are questions.' " No one would say exactly where the statement originated, but State's legal department and Justice Department lawyers who represented the defendants in the Horman case cleared it, according to two State Department sources.

Several members of Congress saw the film earlier this week. "It was a gripping movie," said Sen. Claiborne Pell (D-R.I.), a member of the Senate Foreign Relations Committee, "and a fairly accurate portrayal of the events that transpired during that time -- the people in the streets, the shooting -- but it was too harsh on the State Department."

Costa-Gavras objected to the part of the State Department release that read, "On March 20, 1981, after approximately four years of active litigation, the Plaintiffs voluntarily withdrew their complaint."

"That is not truth," he said.

Edmund Horman said he asked the court to dismiss the suit without prejudice, which means he can bring the suit again. He said he did so because "documents that were vitally important were withheld on the basis of state secrets."

The State Department said that it "provided hundreds of documents to the Hormans and Thomas Hauser" regarding Charles Horman and the circumstances of his death and disappearance.

Said Kessler, "We have documents that have not been given to the Hormans, but there's no information in those documents relating to Charles Horman's death or disappearance that hasn't been made available to the Hormans in an unclassified manner.""The allegation that we didn't help him is just not true," said Nathaniel Davis, the U.S. ambassador in Chile at the time of the coup.

"Oh, they loaned us cars and they were sweet as pie," said Edmund Horman. But, he continued, at the same time U.S. officials were telling him "the highest levels" of the Chilean government had revealed nothing of his son's whereabouts, newspaper reports were quoting neighbors as saying they had seen Charles Horman being arrested.