It's hard to think of a single film in which Tommy Lee Jones stands still. He hit the ground moving as an actor and is still doing it. On screen he pushes through scenes with a bull-necked insouciance, throwing out lines of dialogue to left and right, like a farmer tossing seed, while stragglers strive to keep up.

I see him hustling through The Fugitive in his Oscar-winning turn as a peripatetic marshal; striding through Men in Black doing his dark-suited, don't-stop-me stuff in the alien-ridden US; or in neo-westerns such as Ron Howard's The Missing or his own superb The Three Burials of Melquiades Estrada (opening in Britain this week), bestriding a horse and making it darned clear to laggards that he intends to out-ride them.

What would you expect? Hollywood's quirkiest actor-filmmaker was born to activity and the outdoors. A quarter Cherokee, the son of an oilfield worker, he owns a 4,000-acre Texas ranch for cattle and polo ponies. He played football at Harvard.

He is even a challenging pacesetter, God knows, for an interviewer keen on a word about Burials, which Jones produced, directed and stars in and which won two top awards in Cannes (Best Actor for him, Best Screenwriter for Guillermo Arriaga).

I finally catch up with him after two weeks of "he'll talk", "he might talk" and "forget it" from his PR lieutenants. The Jones boom, that basso americano, lowers itself into place. The Jones face and physique - well, who needs reminding of the chunky build and sandblasted leathery phiz, those features that have stood in for great demons of our time (Howard Hughes, murderer Gary Gilmore) as well as lending dark grace to star roles and vignettes for every auteur from Oliver Stone to Robert Altman.

Jones's newest cameo, playing a company hit-man closing a radio show in The Prairie Home Companion, is hardly a stretch but he says: "I did it to spend time with Bob Altman and to see how good high-definition (digital video) can look on the big screen." It looks great. "It was a weird film," (it is magical surrealism concocted by Altman and Garrison Keillor) "and I loved seeing Meryl Streep sing those country songs. Isn't she great?"

How did Burials come about? Did Jones and Arriaga create it together? Would he call it, with its trek-and-revenge tale of a ranch foreman (Jones) dragging the cop who killed a Mexican friend deep into Mexico to confront him with the realities underlying his race hatred, a modern western?

"I'm not keen on genres, they're labels you stick on films. But if people need a label to convince them to see it, that's fine by me. You could call it a western. By the same principle you could call it a horror film, because there's a dead body, or pornography, because there's nakedness, or comedy, because it's funny as hell. It's about the mechanics of faith, too. So it's a religious-western-horror-pornographic comedy."

Whatever it is, it apparently came about by a two-man epiphany. Jones loved the powerful, prize-winning Mexican film Amores Perros and talked to its screenwriter, Arriaga: "He was interested in making movies about his country and I was interested in making movies about mine." So they spitballed ideas for a story about both countries.

"We visited the Rio Grande and if you spend even a little time round there you see that it's not a river dividing two countries, it's a line across a land that's all one place on both sides of the border. We wanted to say that the same life goes on in the same way, in both places." As well as directing, Jones would play the lead role. "I can wear two hats. When the director is me, I'm very good at giving him what he wants. And I've been at the acting job long enough to know what I'm doing and where I am in any scene."

He has been at it from childhood, with interruptions for sport, manual odd-jobbing and a Harvard major in English literature. "I started acting where we all start: in the backyard at home. Childhood games. Then at Harvard I did Shakespeare, Greek tragedy" - a long list follows - "and acted in the summer too. Theatre was big then in Cambridge [Massachusetts]."

His interests include reading classic literature. "The cannon of American and English drama and fiction is very important to an actor or director. You learn the mechanics of storytelling, how to manage narrative." And how to fashion your own dialogue or character. Jones frequently and creatively does this. In The Fugitive he turned a routine cop role into an irresistible blend of dry humour and martinet bravura - though not, he insists, by ad-libbing.

"Thank you for using the word 'creative'. It's not improvisation. I never improvise. I worked very closely with Andy Davis [director] and Harrison Ford and the other actors to see how we could make the lines better. Humour's very good for drama, it's very important.

But I don't want to move away from his Harvard days without asking him about his famous roommate. Is it true this was Al Gore?

"Yes." Is it also true that he and Gore were joint models for - of all once-famous fictive heroes - Oliver in Love Story, the lovestruck hero of the bestselling novel that became a top-grossing film, both penned by Harvard classics lecturer Erich Segal?

Jones denies it but chuckles. "Erich knew us both, we were in the same fraternity house. But he said this years later, probably to make people laugh or to have something to say to a journalist. Oliver in Love Story was not an Irish-American from California like Ryan O'Neal (who played him in the movie). He was a rich, privileged guy from the east coast. Well, Al was from Tennessee. I was from Texas. Years had gone by and Erich was just looking for something to say." (It's an odd coincidence, nonetheless, that the first feature film Tommy Lee Jones acted in, albeit in a small role, was Love Story.)

Knowing Al Gore in Harvard days, and knowing him still today as Jones does, along with other friends from the leftish-liberal side of Washington or Hollywood (such as Oliver Stone, for whom he has made three films), must tell us something about his own ideological sympathies, mustn't it?

"Everything helps form your attitude in life. I've spoken on behalf of political candidates I believe in" (including a speech at the Democratic Convention for Gore). "But does politics play a part in my films? I don't stand beside my work proclaiming a political position. There are enough filmmakers doing that. A movie has to stand by itself as a movie and to speak for itself."

And an actor can find himself playing roles, from time to time, that exist at an opposite pole to his own views and beliefs. In a 35-year career Jones has played one megalomaniac millionaire (Howard Hughes, in a TV drama), one convicted murderer (Gary Gilmore, in the film of Norman Mailer's The Executioner's Song) and one alleged presidential-assassination plotter (Clay Shaw, in JFK).

Fearlessly, Stanislavskianly, he did the research. He tracked down Hughes's last interviewer, who kept his files "in a basement like something Miss Havisham would live in". He talked to Gilmore's family. Only with Shaw "who was a flamboyant homosexual" - and somewhat freely demonised in Stone's film - did Jones "pretty much use my imagination".

I put to him that JFK was what made Jones a movie star. The Clay Shaw performance was as bold and left-field for him as playing a greed guru in Stone's Wall Street had been for the hitherto sub-stellar Michael Douglas. Jones, though, goes a little defensive. "I don't know about turning points. It's all a continuity. You don't stand outside your career and calculate and assess it like that."

I bet an actor does: just a bit. I bet too - revisiting the arena of political sympathies - that Jones has sometimes wondered, as I do, whether his quarter-Cherokee blood doesn't make his heart pump a little more strongly on behalf of the alienated, the dispossessed, the disadvantaged. "We're all alienated in different ways," he responds. "We can all identify with that state. You don't have to be a native American or a Mexican swimming across a river to be alienated. Some are born alienated. Some have alienation thrust upon them."

Burials clearly is a film about alienation: of many kinds and on many levels. At the centre is the story of two men who move from fanatical mutual alienation into, if not friendship, at least a battered mutual understanding or enlightenment.

"Enlightenment, there you go. It's a journey. Like so many stories or movies. It's the narrative of a learning process."

As cinema itself is. For Jones the biggest pleasure for an actor or filmmaker is to be there when the audience "gets" a film and its idea - when what begins as a small concept in a moviemaker's head becomes a sharing process writ large. "The satisfaction starts in sitting down at a table working out your thoughts, putting your ideas for the character or film on paper. Then you bring it to the camera. Then you sit with an audience that's all laughing, or all crying, all thinking together. You're in the same room, hundreds of you, having the same experience. That's the big satisfaction."