IN addition to making movies that galvanize the emotions in ways that can be simultaneously fascinating and infuriating, Costa-Gavras, the Greek-born, French film maker (»Z,» »The Confession»), also has a knack for stirring up publicity from the most unlikely sources.

In 1973 his »State of Siege,» which accused an official of the United States Agency for International Development of teaching torture methods to repressive right-wing regimes in Latin America, was booked into the Kennedy Center for the Performing Arts in Washington, for a gala showing by the American Film Institute. At the last minute the showing was canceled when someone decided that it might not be an especially appropriate film for presentation under such auspices.

Now »Missing,» Mr. Costa-Gavras’s latest film, which is about the 1973 kidnap and murder in Chile of Charles Horman, a young, Harvard-educated, counterculture journalist, is opening today at the Beekman Theater, two days after the release of a most unusual statement by the State Department. The department takes issue with a number of facts in the film and just about all of its conclusions.

It is the belief of Mr. Costa-Gavras, as well as of Thomas Hauser, the lawyer who wrote the book on which the film is based, that young Mr. Horman was executed by Chilean authorities, probably with the tacit approval of some United States representatives on the scene, because he had knowledge of United States involvement in the military coup that had overthrown the Marxist government of Dr. Salvador Allende Gossens, the Chilean Presi dent.

About the only fact not in dispute is that Mr. Horman, immediately after the coup, somehow became one of the victims of the roundup and execution of hundreds of Chilean left-wing activists and sympathizers.

Mr. Costa-Gavras seems to ask for such controversy. The film opens with a statement to the effect that »Missing» is »a true story» and that all of »the incidents and facts are documented.» If all of the incidents and facts are really documented, then it should follow that the conclusions drawn cannot be open to too much question. This is something that I think even Mr. Costa-Gavras would not say, though by the end of the film, there is certainly no doubt about what he thinks.

Further complicating these questions is that »Missing» is Mr. Costa-Gavras’s most beautifully achieved political melodrama to date, a suspense-thriller of real cinematic style, acted with immense authority by Jack Lemmon, as Charles Horman’s father, Ed Horman, and Sissy Spacek as Charles’s wife, Beth. The screenplay, by Mr. Costa-Gavras and Donald Stewart, is a model of its kind, in which Ed and Beth’s search for Charles is developed in a series of scenes that seamlessly join past and present actions into a nonstop, forwardmoving narrative.

The center of the film is the political awakening of Ed Horman, who comes to Chile to help Beth, though he suspects that Charles has gone under cover for some reason that is beyond his comprehension. »If he had stayed home,» says Ed, who is well-to-do and politically conservative, as well as a practicing Christian Scientist, »this wouldn’t have happened.»

Ed calls Charles »almost deliberately naive» for his identification with underdogs. Says the beleagured Beth, »We’re just two normal, slightly confused people trying to connect with the entire enchilada.»

Charles, played with modest simplicity by John Shea, comes to life in the flashbacks. He’s a dedicated, somewhat guilt-ridden heir to a privileged America, a young man who reads »The Little Prince» for literary inspiration and whose optimism is unshakable. If not deliberately naive, he’s the kind of unsophisticated saint one always wants to believe in.

Ed and Beth’s search for Charles involves a succession of chilling encounters with politely patronizing United States embassy and consular officials, as well as with members of the Chilean Government. The major villains are vaguely identified United States military people, especially a Capt. Ray Tower (Charles Cioffi), who befriends Charles, and a young American woman named Terry Simon (Melanie Mayron), when the two are marooned in the resort town of Vina del Mar during the coup, unable to return to Santiago.

If »Missing» were only an inventory of the details of Charles’s life and disappearance, it wouldn’t have the terrific emotional impact that it has. Mr. Lemmon and Miss Spacek are superb, however, and their increasing respect and fondness for each other as the story unfolds gives »Missing» an agonizing reality.

Mr. Costa-Gavras also knows Chile, where he filmed »State of Siege» during the Allende regime – »Missing» was shot in Mexico – and he is particularly successful in evoking the looks, sounds and feelings of a society in upheaval.

There’s a stunning sequence in Santiago when Beth, unable to get home before curfew, spends an endless night hiding in an alley, hearing in the distance gunfire and other sounds not easily identified. At one point a terrified white horse goes galloping down an otherwise deserted street, pursued by soldiers firing random shots from a speeding jeep. In this sequence as elsewhere, the camera work by Ricardo Aronovich is very fine indeed.

Whether or not its facts are verifiable, »Missing» documents, in a most moving way, the raising of the political consciousness of Ed Horman who has, until this devastating experience, always believed in the sanctity of his government and accepted its actions and policies without question. Among other things »Missing» does is to convince you that, next time, you’re not going to waste your vote. The passive citizen is the citizen-victim.

In view of the film’s opening contention of being a true story, the care that Mr. Costa-Gavras takes not ever to identify Chile by name is a bit disingenuous. The cities are clearly named and identified. Also a bit disingenuous is the way the film never bothers to give a good answer to the question of why the Chilean – and possibly the American – authorities found it necessary to liquidate Charles Horman while allowing the safe departure from Chile of Terry Simon. Terry, after all, is privy to all the supposedly damaging information Charles gathered in Vina del Mar.

These are valid questions to raise about a film that is so fine that one wants it to be above reproach.

»Missing,» which has been rated PG (»parental guidance suggested»), contains several harrowing scenes of violence, as well as a s equence in a Santiago morgue that could inspire nightmares in adults as easily as in the very young.

A Parade of Why’s

MISSING, directed by Costa-Gavras; screenplay by Mr. Costa-Gavras an d Donald Stewart; director of photography, Ricardo Aronovich; f ilm editor, Fran,coise Bonnot; music by Vangelis; produced by Edward Lewis and Mildred Lewis; released by Universal Pictures. At the Beek- man, 65th Street and Second Avenue. Running time: 122 minutes. This film is rated PG.

Ed Horman . . . . . Jack Lemmon

Beth Horman . . . . . Sissy Spacek

Terry Simon . . . . . Melanie Mayron

Charles Horman . . . . . John Shea

Capt. Ray Tower . . . . . Charles Cioffi

Consul Phil Putnam . . . . . David Clennon

United States Ambassador . . . . . Richard Venture

Col. Sean Patrick . . . . . Jerry Hardin

Carter Babcock . . . . . Richard Bradford

Frank Teruggi . . . . . Joe Regalbuto

David Holloway . . . . . Keith Szarabajka

David McGeary . . . . . John Doolittle

Kate Newman . . . . . Janice Rule

Congressman . . . . . Ward Costello

Maria . . . . . Tina Romero

Statesman . . . . . Richard Whiting

Photo: photo of Jack Lemmon in »Missing»