Among the better internet-fuelled rumours about Gabriel Byrne is that he was once a matador. "Let's just put that down to myth," he sighs, settling back into a chair. The closest he ever got was during a brief time living in Spain, when he met an Englishman who gave bullfighting lessons. "He was completely hopeless. There were 10 students - three women and seven men, equally as bad as he was. We never actually came in contact with a real bull. It mostly consisted of him with a pair of fake horns running at us - and we paid a lot of money for this. I was foolish enough to think that you could study bullfighting in 12 weeks with an Englishman who was never in the bullring."

But, like any good matador, Byrne always seems one step ahead of expectations. As Steven Spielberg once told him, he was never sure whom the actor would play next. If the extreme example was when Byrne went from a priest in Stigmata to a sexed-up Satan in End of Days, his whole career has always been about sidestepping audience expectations. "I've always lived my life on instinct," he tells me.

Byrne didn't go to America until he was 37, when he followed his wife-to-be, actress Ellen Barkin, back there after they got together on the set of Spanish-made Siesta. They married a year later in 1988, at 3am in a Las Vegas registry office. The couple have two children, Jack and Romy, but their relationship did not last: they separated in 1993 (though did not divorce for another six years).

It was Barkin who recommended that Byrne audition for 1990's gangster saga Miller's Crossing by Joel and Ethan Coen. By this point, he had already spent the best part of the previous decade toiling away in film - most notably playing Byron in Ken Russell's Gothic. But it was as a manipulative mobster for the Coens, coupled with his turn as one of The Usual Suspects in Bryan Singer's crime classic five years later that brought him to the attention of Hollywood. Much of what was on offer was standard-issue: Winona Ryder's love interest in Little Women, D'Artagnan in The Man in the Iron Mask, the captain in the risible Ghost Ship and so on.

"I did my clutch of Hollywood films," he shrugs. "I got to live in Hollywood and got to be a Hollywood actor, I suppose." He says it like it's a dirty word. "There's a tremendous pressure in Hollywood to be a certain kind of actor, a certain kind of star. And that unless you're in that category of star, in some way you're unsuccessful. I don't believe that anymore." He returned to "making films with directors I felt were cutting-edge" - notably with David Cronenberg on Spider, which found the actor in, well, bullish form as a booze-sodden father.

This month sees Byrne deliver another impressively calibrated performance in Jindabyne, a take on the Raymond Carver short story "So Much Water, So Close To Home", previously seen as part of Robert Altman's Carver anthology Short Cuts. Directed by Ray Lawrence, who won plaudits for his 2001 film Lantana, it tells the story of four men - including Byrne - from the eponymous town in the Australian Snowy Mountains, who head out on a fishing trip only to discover the corpse of an Aboriginal woman floating in the water. Rather than report it, they tie her up and continue fishing, a reaction that sends shock waves through the community when they return.

The bulk of the film deals with the impact this event has on the marriage between Byrne's character Stewart, a blue-collar ex-pat Irishman who first finds the dead body, and his wife Claire (Laura Linney). "In every scene in the film, there's conflict, and contradiction and ambiguity," says Byrne. Jindabyne is not aimed at the 18-24 demographic that most studios seem to court. "I think you would have to have experienced some of the feelings and understand something of the themes of it. I don't think you might understand those themes at 18 or 19 completely. It's not cut for that kind of an audience. They want action. They don't necessarily want emotion."

Dealing with the way men confront their feelings - be it sorrow, anger or fear - Jindabyne, according to Byrne, takes the uncommon step of examining it close up. "Men are not encouraged to weep, to cry," he says, "yet the emotional life of most men is extremely complex, rarely discussed and rarely examined in films. The way the culture demands that a man react is usually through silence, anger, and rage or to be withdrawn. Whereas women tend to be emotionally more confrontational and more freely able to express their feelings, and one of the themes of this film is how men and women react to trauma."

Byrne evidently sees himself in these terms. He tells me he only recently saw a dead body for the first time, a friend who died, and for years couldn't face the idea. "When my mother and my father died, I deliberately did not look at the bodies because I did not want it as the last memory I had of my mother and father. But in the tradition of the Irish funeral, the body is left out for people to look at because the purpose of it is to look at what death is, so life becomes more important. And I always thought about why I didn't look at that body of my father or mother.... so in the film I couldn't think of anything more scary than turning a dead woman over and looking at her naked body."

He was born in Dublin, the eldest of six. "I'm what they call a recovering Catholic." While growing up, he wanted to be a priest and spent four years at a Catholic seminary in Birmingham. He was expelled "due to the presence of women, alcohol, cigarettes and football", he says. "I don't think I'd have made a very good priest. The things I wanted to do were all surface things: to dress up and hear confessions and say communion, but I didn't want to spend seven years training to do it. I suppose it was a suppressed form of wanting to be an actor."

Acting wouldn't come for at least another decade, by which time Byrne had spent nine years teaching Spanish and Gaelic literature. "I had no ambitions of being an actor at all," he says. "Teaching was always something I wanted to do. I love to be able to communicate with kids. But when I was teaching I felt I didn't really know anything about those subjects." He didn't start acting professionally until he was 29. "I went into acting at night time because I didn't want to spend my free time in pubs, which was the only place people seemed to congregate."

Admitting he also gravitated towards acting "to meet women", Byrne began his career on stage in a Dublin production of The Importance of Being Earnest before eventually graduating to London's Royal Court and National theatres. "I never went to drama school so I never had any sense of any acting style," he says. His heroes were close to home - actors such as Alan Bates, Albert Finney and Richard Harris.

During this time, Byrne become something of a local heartthrob after appearing in popular soap The Riordans. He recalls going to his father's house, with his brothers, sister and mother to watch the first episode: "My father looked at this thing, his favourite show that had been running for 18 years, and his son walks onto the screen. And he just sat looking at the television. The theme music came up, and he looked around and said, 'Television - a wonderful thing, all the same. There you are [pointing to the screen, then turning to his son] and there you are!'"

Living in New York now to be with his children, Byrne still is deeply attached to his Irish roots. You only have to look at the films he's produced. He began with Mike Newell's 1992 film Into the West, in which he played a gypsy traveller. Then there was the Oscar-nominated In The Name of the Father based on the autobiography of Gerry Conlon, an Irish thief falsely imprisoned for planting an IRA bomb in London. More recently, the Irish-set coming-of-age story The Last of the High Kings, which Byrne co-wrote, and the Second World War-era drama The Brylcreem Boys have occupied him.

He says he has a hankering to quit the business and return to teaching full-time. "Acting is a very satisfying way to make a living but it's not life," he says. "I don't want to spend my life on movie sets and wake up at 70 and say 'Where's my life gone?' I know people like that and I don't want to end up like that - the horror of being somebody that the movies sucked dry."

'Jindabyne' opens on 25 May