Paul Greengrass's verité-style depiction of events aboard the fourth plane on 9/11 has been acclaimed as a triumph. Donald Clarke talks to the director

EVERY now and then a film arrives whose influence extends beyond the multiplex and into op-ed pages, parliamentary debates and - does this still happen? - pulpits. Such films often come to stand for the historical events or myths that inspired them. What you thought about The Passion of the Christ, 2004's more-than-a-movie, said as much about your religious beliefs as it did about your views on cinema.

Paul Greengrass, the director of Bloody Sunday and The Bourne Supremacy, could have been in little doubt that United 93 would turn out to be just such a film. Telling the story of the flight from Newark to San Francisco which, following its hijacking on September 11th 2001, crashed in Pennsylvania, killing all passengers, this harrowing picture risked offending and appalling a great many people. As it happens, when United 93 screened at the recent Tribeca Film Festival before an audience including relatives of those who died in the disaster, it was universally acclaimed a triumph.

I suppose he is a relieved man, but it is hard to tell. Greengrass's cinematic style may be feverishly agitated, but the man himself is calm, softly spoken and infuriatingly ruminative. Emerging from the reliably left-wing world of 1970s television documentary - he worked on the legendary World in Action for ITV - he would, in a more predictable world, come across like an angry firebrand. The reverse is the case.

"Yes, I was relieved," he says, when I ask about that first screening. "What is interesting when you meet victims of political violence - whether the victims of Bloody Sunday or United 93 - is that they all have a desire to go through a journey and discover meaning in these events. We don't want to go on that journey. We want to go on with our lives. We want the World Cup to come along. We want to go on our holidays. What we want is to be shocked by these events and then move on. What binds these victims is that they don't want people to move on. They want these stories to remain."

United 93, filmed in the same faux veritéstyle as Bloody Sunday, is a searing, grimly impressive piece of work. But there are questions to be asked about it. There is little dispute about what happened on the ground. And the fascinating sections in the air-traffic control centre - based, one assumes, on reliable documentary sources - have the indisputable air of authenticity about them. When, however, the film turns to the events in the air, supposition takes over. Who knows which passengers came together to take over the plane? Are we even sure that United 93 crashed as a result of such an insurrection? The film is an unusual mix of docudrama and, well, drama.

"Of course you are right. We cannot know exactly what happened," says Greengrass. "When I speak at film schools I always explain they must never defend their film by saying: this is what actually happened. It's not what happened. What happened is the story itself. Whether you use a well-worked screenplay or the style we use, the film remains an artefact."

Greengrass, as is his wont, then meanders off onto a lengthy digression about the merits and demerits of the artificial construct in factual cinema. Eventually he comes back to the issue. "My methodology in this case remains the 9/11 Commission Report." On those words the ears of a million conspiracy theorists prick up. Since the film's release, a great many people who spend too much time on the internet have been denouncing Greengrass as a stooge of the military-industrial complex. Only a mid-air explosion could scatter the debris over such a wide area, they say. A white plane was seen tailing United 93. The entire 9/11 disaster was engineered by agents of the US government as a way of justifying the invasions of Iraq and Afghanistan. On and on come the supposed plots and anomalies.

In a recent piece in the Guardian, Alex Cox, the English director of Sid and Nancy and Repo Man, referred to an internet blog which argued that basing such a film on the 9/11 Commission Report would be akin to basing Bloody Sunday on the Widgery Report (the British judiciary's whitewash of the paratroopers' role in the Derry slaughter). Suddenly, the heretofore laid-back Greengrass becomes positively animated.

"I can tell you one thing: Alex Cox has never read the Widgery Report and he has certainly never read the 9/11 Commission's report," he puffs. " I admire Alex Cox. He has always been an iconoclastic force. But I saw that and I thought it was a shameful piece of nonsense. He should be ashamed of himself. It was an appalling smear on me."

Shaking off his jet lag, he goes on to compare the meticulousness of the 9/11 Commission report with the shoddiness of Widgery. The former, he claims, made an honest attempt to discover what happened, while the latter was a feeble cover-up.

"The second point to make is that the conspiracy theories are, for the most part, crap," he angrily continues. "They are just not true. United 93 was not shot down. It is simply not true. The defence forces could only get four planes in the air. That's the real scandal, not these malevolent forces supposedly controlling our lives. You have this multi-million dollar defence industry and they could only get four planes in the air. They didn't even know about 93 when it crashed."

The director, an avowed opponent of the war in Iraq, may find it easy to dismiss the negative responses from ranters on the internet. But he must, surely, feel uncomfortable about the way certain ultra-conservative forces have used the picture as a way of justifying George Bush's bellicose foreign policy.

"It is my opinion that the kook-fringe left will come away from this movie blaming Bush," Rush Limbaugh, the right-wing radio personality, recently declared. "But anybody with half a brain cannot help but just be angry with the terrorists. And this movie is going to refocus, for those who see it, the exact reason we are in the war on terror."

Bravely, Greengrass agreed to appear on Limbaugh's show. "Yes. I told him I must be the first long-haired liberal to ever appear on the show," he laughs. "Immediately 9/11 happened it was corralled by politicians and, yes, I did have the fear that, going full circle, the film might be too. But I wanted to address the low-level fear that it caused and I did not want to be dissuaded by the knowledge that some parts of the story might be owned by people whose political views I disagreed with."

The chaos and terror that the film depicts - Greengrass's camera is one of world cinema's shakiest - goes some way to counteracting the popular myth that the passengers on Flight 93 acted in coolly heroic fashion. "Let's roll," the supposed last utterance of Todd Beamer, since misused by rock stars and college football teams, is muttered rather than proudly bellowed. "Those words became almost a political slogan," Greengrass says sadly.

But, for the most part, the relatives of the dead, who were consulted throughout the film-making process, seem happy with the end result. "I talked with them at great length and tried to work out what the important issues were from their perspective," he says. "And then I had to be honest with myself and try to discover where their views intersected with what I wanted to say." But not force them to intersect? "Exactly. That is the challenge."

United 93 emerges as a towering achievement. Beginning with the mundane procedures of a few dozen average lives, it ends with the bleakest and most desperate of struggles. Even if its version of events is difficult to verify, it is undeniably valuable as a memorial to the dead. The events on the plane also, in Greengrass's mind, serve as a metaphor for the state the world finds itself in today.

"There is no question that those people were exceptionally courageous," he says. "Not least because they were ordinary people. They had almost no chance of having a successful outcome. They either had to sit there and die, or move and die. What I think is that we, who have the luxury of not being in that terrible position, have broader choices to make. We should work hard to find the right solutions for our own aeroplane, for our world to day, and hopefully we will all get through this."

United 93 is released next Friday