Is James Salter America's most important living writer? The question might sound absurd yet no less than Richard Ford and Susan Sontag think his work superior to that of the Nobel prize-winners Toni Morrison and Saul Bellow. Given that Salter has published only five novels and a prize-winning short story collection in 40 years of near-invisibility, it might be fairer to echo the New Yorker critic James Wolcott and call him America's most underrated underrated writer.

Salter's long-overdue autobiography, Burning the Days, a stylish and moving account of his various incarnations as a fighter pilot, rock climber, screenwriter and novelist, may help bring him the wider acclaim his fiction deserves. The book arrests your attention from its disarming opening: "The true chronicler of my life, a tall, soft-looking man with watery eyes, came up to me at the gathering and said, as if he had been waiting a long time to tell me, that he knew everything. I had never seen him before."

Salter's chronicler turns out to be a post office worker, the portentously titled Historian, who recites intimate details of the author's life, some of which are artfully culled from the local papers. Salter's chief concern is with the reality of fiction, with the way our lives can be shaped and even destroyed by a fidelity to certain literary ideals and conceits. In the memoir, the Historian is eventually led away by his wife, baffled by his inability to fill the gaps and omissions in his own narrative.

Burning the Days is written in the heroic language of an American memoir (one thinks of Nabokov's Speak Memory) yet takes its place in a recognisably national tradition. The blur of snow and trains forming the backdrop to Salter's early life recalls Nick's journeys home in The Great Gatsby, or George Willard's departure from Winesburg, Ohio, in Sherwood Anderson's novel of the same name. Salter's experiences are essentially archetypal - a "flaring of America" to use his phrase - his prose spare and imagistic. His descriptive writing is careful, too careful, as when he describes a "defiladed road"; but his metaphors are daring.

Salter's carefulness is probably a product of his days as a cadet at West Point, a place where "the terrible ring of metal hitting the floor - a breast-plate that had slipped from someone's hand - was a sound like the dropping of an heirloom". He graduated too late to fight in the second world war, his ship sailing for the South Pacific under a banner strung from the Golden Gate Bridge that read "Welcome Home Heroes". But Salter was to fight in the Korean war, something he evokes with breathtaking precision. Burning the Days falters once Salter resigns his commission to become a writer, descending into a kind of Fitzgerald-like pastiche; but there are some lovely anecdotes as compensation.

Literature, Kenneth Burke wrote, is "equipment for living". Salter's career appears grounded in a desire to fulfil that grand proclamation. "My ideal is a book that is perfect on every page," he told an interviewer, "that gives you tremendous aesthetic joy on every page." Yet we live in an era when such ambition is distrusted and novels are praised for being merely readable. The sports page is readable (I would choose it over almost anything else at breakfast); Nick Hornby is readable. But they are not equipment for living.

Salter's novels are available in their entirety to a British audience through the foresight of the Harvill Press, including his newly re-issued debut, The Hunters (1956). The author disowned the work some years ago, but he was wrong to do so: it is a gripping and lucid account of how war can generate "a furnace of the individual".

His major theme is the longing for fame, a desire that runs through all his work. "He wanted one thing, the possibility of one thing: to be famous. He wanted to be central to the human family, what else is there to long for, to hope?" The words are spoken by the hero of Light Years (1975), and can be read as a painfully ironic judgement on Salter's baffling neglect by the literary world. Both this and his other major work, A Sport and a Pastime (1967), sold poorly, the result perhaps of some devastating reviews, despite being hailed as the work of genius by a small minority.

Light Years is an impressive, if slightly overwritten, study of the failing marriage of two middle-class New Yorkers.The couple live "a Russian life, a rich life, interwoven, in which the misfortune of one, a failure, an illness, would stagger them all". As a work of ambition it aspires towards the luminous quality of Woolf's To the Lighthouse - Viri is "a man lying fully clothed in the stream of days". But the prose is, if anything, too precise, too ornate. Salter often writes in a kind of eternal present - "the sea is quiet and white . . . The beach is deserted . . . the sand is warm" - which gives his work a mythic quality not entirely reconcilable with human passion and pathos.

Salter's desire to encompass reality is one shared by the unnamed narrator of A Sport and a Pastime, who describes his story as "notes to photographs of Autun", the French town and setting for this disturbing erotic work. The narrator's project is a tribute to the photographer Atget, who took innumerable photographs of Paris in the early part of the century, slowly stealing the city from its inhabitants. The German critic Walter Benjamin described Atget's pictures of deserted streets as "crime scenes", and Salter's novel unhinges our notions of guilt and innocence in its urgent description of the love between a teenage French girl and a Yale drop-out.

Salter's prose is not without fault: his striving after a kind of stuffed perfection leads him into a rarefied realm, where the air is too thin to breathe and ideas are not always thought through. His work lacks humour, too. But this can hardly justify his strange neglect. In A Sport and a Pastime the narrator describes his story as "a fiction for which a place already existed in his heart". Reading James Salter is just such an experience.

Stuart Burrows is a British critic based at Princeton University