Greta Garbo, the enigmatic and elusive star of some of Hollywood's most memorable romantic movies of the 1930's and a 50-year focus of curiosity and myth, died yesterday at New York Hospital in Manhattan. She was 84 years old.

A hospital spokesman, Andrew Banoff, saying he was respecting the wishes of the family, provided no details of her death, and said services would be private.

The Swedish-born actress had a classic beauty and a natural talent for conveying deep emotions before a camera. Her performances in such classics as ''Anna Christie,'' ''Grand Hotel,'' ''Queen Christina,'' ''Anna Karenina,'' ''Camille'' and ''Ninotchka'' were an arresting mix of urbaneness and vulnerability, with a glint of mockery.

The Screen's Great Sufferer

The finest element in a Garbo film was Garbo. She invariably played a disillusioned woman of the world who falls hopelessly and giddily in love. Tragedy is often imminent, and her tarnished-lady roles usually required her to die or otherwise give up her lover. No one could suffer like Garbo.

Mysterious and aloof, she appealed to both men and women, and she exerted a major influence on women's fashions, hair styles and makeup. On screen and off, she was a remote figure of loveliness.

Garbo's career spanned only 19 years. In 1941, at the age of 36, she made the last of her 27 movies, a slight comedy called ''Two Faced Woman.'' She went into what was to be temporary retirement, but she never returned to the screen.

Yet generations later, her best movies were shown on television, in sold-out retrospectives and in revival houses, and she remained one of the greatest screen actresses, evergreen, eternally young.

In the 1930's she was called ''the screen's first lady,'' the standard against whom others were judged. Andre Sennwald wrote in The New York Times that she was ''the most miraculous blend of personality the screen has ever seen.'' Alistair Cooke termed her ''every man's fantasy mistress.'' The French called her ''La Divine.'' And Kenneth Tynan concluded, ''What when drunk one sees in other women, one sees in Garbo sober.''

For more than half a century, the actress remained an enigma, ''the Swedish sphinx,'' because of her deep fear of reporters and other strangers and her insistence on guarding her privacy. Ironically, in seeking to avoid publicity, she became one of the most publicized women in the world.

Her penchant for privacy broke all of Hollywood's rules, said her biographer, John Bainbridge. Except at the start of her career, he wrote in ''Garbo,'' she ''granted no interviews, signed no autographs, attended no premieres, answered no fan mail.''

A declaration often attributed to her was, ''I want to be alone.'' Actually she said, ''I want to be let alone.''

Her screen image was exotic and inscrutable, while her private life was simple, even mundane. In a rare statement to reporters she acknowledged, ''I feel able to express myself only through my roles, not in words, and that is why I try to avoid talking to the press.''

Garbo's aloofness frustrated the press, which published thousands of photographs of her frantically clutching a drooping hat over her face as she shopped or raced for a train, ship or plane.

Speculations About Her Escorts

Her presumed love affairs - she was never known to have married - were the subject of voluminous gossip and speculation. Over the decades her frequent escorts included the actor John Gilbert; the conductor Leopold Stokowski; the nutrition theorist Gayelord Hauser; Baron Erich Goldschmidt-Rothschild, an art connoisseur, and George Schlee, a figure in haute couture.

Garbo's movies earned her more than $3 million, a record at a time of low income taxes, and her frugality and astute investments, particularly in Manhattan real estate, increased her wealth. Her life had begun in virtual poverty.

Greta Lovisa Gustafsson was born in Stockholm on Sept. 18, 1905, the daughter of Karl Alfred and Anna Lovisa Gustafsson. Her father was an unskilled laborer of peasant stock who was often out of work.

The family lived in a shabby district of Stockholm, and Greta had to leave school at the age of 13 to help care for her seriously ill father. Every week she took him to a charity clinic, where they had to wait hours for his treatment. She vowed to build her life so she would never be financially dependent.

Her father died when she was 14 and she had to go to work, first as a latherer in a barber shop and then as a salesclerk in a department store.

Her beauty soon gained her a role in a short film sponsored by the store, a part in a publicity short for a bakery and then a leading role as a frolicking bathing beauty in a slapstick feature, ''Peter the Tramp.''

She won a two-year scholarship to Stockholm's Royal Dramatic Theater Academy, where she was discovered by Mauritz Stiller, a famous, worldly and flamboyant director. He and Victor Seastrom were the leaders of the golden age of Swedish silent movies.

The 40-year-old Mr. Stiller took absolute command of the professional and private life of the 17-year-old novice. He named her Garbo and cast her as the ingenue in his film epic of Selma Lagerlof's novel ''Saga of Gosta Berling.''

Doubts in Sweden, A Hit in Berlin

The four-hour movie drew mixed notices in Stockholm, but a three-hour version was a hit in Berlin, where reviewers found Garbo ''a soul-revealing Nordic princess.'' Her next role was as a poor prospective prostitute in ''Streets of Sorrow,'' directed by G. W. Pabst.

Louis B. Mayer, the production chief of Metro-Goldwyn-Mayer, saw ''Gosta Berling'' in Berlin and offered Mr. Stiller a contract. He accepted on condition that his plump protegee also be hired. Mr. Mayer agreed reluctantly, muttering, ''In America, men don't like fat women.''

The first of Garbo's 24 Hollywood movies, all made for M-G-M, was ''The Torrent,'' a 1926 melodrama starring the Latin lover Ricardo Cortez. The daily rushes revealed the young actress's extraordinary film-acting talent, and her salary was raised before the movie was released.

As soon as a camera began rolling, the awkward girl with the moody eyes and large hands suddenly and charismatically sprang to life. Now slimmer and only 20, she played a seductive Spanish peasant who becomes an opera star. She was an overnight sensation.

Mr. Stiller, still smarting from being barred from directing ''The Torrent,'' began directing her in ''The Temptress,'' a variation of ''The Torrent'' starring another Latin, Antonio Moreno. The director had repeated arguments with M-G-M executives and was abruptly dismissed in mid-shooting. He went to Paramount Pictures, but soon also antagonized executives there, and they let him go. Unable to hold a job in Hollywood, he returned to Sweden in 1928. Within a year, he died of several ailments at the age of 45.

His death devastated Garbo, who was said to feel deep guilt for many years for not returning to Sweden to see him. His dynamic personality set the pattern for her later lovers.

A Movie Succeeds And Rumors Fly

Her third Hollywood role was a heartless adulteress in ''Flesh and the Devil,'' co-starring John Gilbert, the epitome of silent-movie masculinity. Their love scenes, peppered with suggestive gestures and language, were electrifying. Reports of a Garbo-Gilbert romance swept the country, and their passionate on-screen lovemaking was regarded as a reflection of their off-screen lives. The gossip fueled the movie's triumph.

M-G-M then co-starred the couple in ''Love,'' a 1927 modern-dress version of Tolstoy's ''Anna Karenina,'' another huge success.

In only two years, Garbo became a superstar. By shrewd negotiating, threatening to return to Sweden and staging a strike, she also won unheard-of raises. In only three years, her weekly salary soared from $350 to $5,000, and six years later she won a record $270,000 per movie.

She made seven more silent films in two years, ''The Divine Woman,'' portraying Sarah Bernhardt; ''The Mysterious Lady''; ''A Woman of Affairs,'' which was adapted from the novel ''The Green Hat'' by Michael Arlen; ''Wild Orchids''; ''The Single Standard,'' and ''The Kiss.'' All made money despite the new dominance of sound movies.

Off screen, there were continuing rumors of a Garbo-Gilbert love affair, with photographers invariably dogging them. There was gossip about an abortive elopement and reports of a wedding ceremony at which she failed to appear. At any rate, apparently weary of the actor's overbearing bravado, she ended the relationship in 1929.

Talkies were destroying the careers of many Europeans, and M-G-M delayed Garbo's sound debut more than two years. She was astutely presented in an adaptation of Eugene O'Neill's ''Anna Christie,'' where her accent was appropriate. The publicity slogan was simply: ''Garbo Talks!''

Her speech was heavily accented and husky, but this new dimension of the Swedish enigma gave her even greater stature, and the movie played to packed houses across the country. Her opening line of dialogue was widely quoted and became classic:. She wearily enters a waterfront saloon and orders the bartender to ''Gimme a visky with chincher ale on the side and don't be stingy, baby.''

Garbo's other early sound movies included ''Susan Lenox: Her Fall and Rise'' (1931), co-starring Clark Gable; ''Mata Hari'' (1932), with Ramon Novarro, and a version of Luigi Pirandello's mystical play ''As You Desire Me'' (1932), co-starring Melvyn Douglas, in which she adroitly portrayed an amnesiac.

An adaptation of Vicki Baum's novel ''Grand Hotel'' featured four other stars John and Lionel Barrymore, Joan Crawford and Wallace Beery but Garbo, as a fading ballerina, stole the movie. The film, directed by Edmund Goulding, won an Academy Award as the best picture of 1932.

M-G-M honored Garbo's distaste for publicity and her insistence that all visitors be barred from her sets. When close-ups were shot, black screens were placed around Garbo and the camera. Asked why she objected to visitors, she said: ''When people are watching, I'm just a woman making faces for the camera. It destroys the illusion.''

Questioned about the screens, she said, ''If I am by myself, my face will do things I cannot do with it otherwise.''

Old Co-star Tries To Regain Career

Despite these demands, her directors and other associates respected her thorough professionalism and lack of temperament and admired her graciousness.

''Queen Christina'' (1933) gave Garbo a long-sought chance to portray the eccentric 17th-century Swedish monarch. She co-starred with Mr. Gilbert in an effort to bolster his sagging career. Sound had revealed his thin voice, totally inadequate for his image of a dashing lover. He did well in ''Queen Christina,'' but his career continued to wither. He drank heavily, and died of a heart attack in 1936 at the age of 41.

The largely fictional ''Queen Christina'' provided Garbo with one of her most radiant roles. The tragic film ended with an enormous five-and-a-half-second-long close-up of her face as she stood on the prow of a ship. The queen has given up her throne for her lover, who is now dead. She is taking his body back to Spain and then faces a voyage to nowhere.

Her breathtaking and mystical expression has often been likened to that of the Mona Lisa. Rouben Mamoulian, who directed, told her the audience must use its imagination to interpret her thoughts, and instructed her ''to make your face a mask, to think and feel nothing.''

Recalling the movie after 50 years, Mr. Mamoulian revealed in a 1983 interview that Garbo had often directed herself. ''When we got to the first intimate scene, she asked me to leave the set.'' he said. ''I asked her why. She said, 'During these scenes I allow only the cameraman and lighting man on the set. The director goes out for a coffee or a milkshake.' I replied, 'When I'm directing a movie, I don't go out for a milkshake.' Reluctantly, she agreed I could stay.''

Garbo's title roles in ''Anna Karenina,'' with Fredric March, and an adaptation of Alexandre Dumas fils's ''Camille,'' co-starring a youthful Robert Taylor, were two of her finest performances. They won her the New York Film Critics Awards for best actress in 1935 and 1936.

She never received an Oscar for best actress. But in 1955 the motion picture academy sought to make amends by awarding her a special Oscar for ''a series of luminous and unforgettable performances.''

Comedy Is Tried To Reclaim Fans

By the late 1930's Garbo's box-office appeal was declining, and M-G-M's solution was to have her do her first comedy. The vehicle was ''Ninotchka,'' a brilliant satire written by Billy Wilder, Charles Brackett and Walter Reisch and directed by Ernst Lubitsch. Garbo superbly played a humorless, self-absorbed Soviet envoy who is humanized by Paris and the urbane Melvyn Douglas. The slogan for the 1939 movie read, ''Garbo Laughs.''

Her second comedy was ''Two Faced Woman,'' a frivolous, heartless farce and her only unsuccessful movie. Meanwhile, the European market, which provided the major income from her pictures, was largely cut off by World War II, and M-G-M refused to meet her salary demands. She announced her retirement.

During the war, Garbo was criticized for not aiding the Allies. But in 1976, in a book titled ''A Man Called Intrepid: The Secret War,'' William Stevenson disclosed that she had helped Britain by identifying high-level Nazi sympathizers in Stockholm and by providing introductions and carrying messages for British agents.

Garbo hoped to return to movies after the war. There were repeated reports over two decades of projects that were to include her, but, for various reasons, none ever materialized.

In later years, Garbo called herself ''a wanderer'' and traveled often to Switzerland, the French Riviera and Italy, though she became an American citizen in 1951. For more than 40 years her home base was a Manhattan apartment on East 52d Street, overlooking the East River.

She was as secretive about her relatives as about herself, and the names of her survivors could not immediately be learned.

Usually alone, Garbo regularly strolled, shopped and browsed in the East 50's and 60's, where New Yorkers savored fleeting glimpses of her haunting face. She wore fashionable but simple outfits, large hats and flat shoes and almost no makeup.

The occasional descriptions of her offered by friends suggest she had a childlike innocence and was selfish and self-absorbed. They deplored the aimlessness of her life. But another friend, Jane Gunther, said, ''She has a poetic magic, so difficult to describe, and all one knows is that one wants this in one's life.''

Assaying Garbo's art and life, John Bainbridge offered this tribute:

''She did nothing that was second-rate. She had dignity and nobility. Like so many great actresses, she may never have possessed a particle of intellectual power, but she had genius before the camera because she was guided by a secret, sublime, infallible instinct to do the right thing in the right way. So unerring was her instinct that it produced the illusion of a most subtle intelligence.''