Elia Suleiman: Hey, heard the one about the firebomb?

Few people see the funny side of the turmoil in Jerusalem, but the Palestinian director Elia Suleiman has the extraordinary nerve to turn it into a deadpan absurdist comedy. In his new film Divine Intervention, a suburban garden is firebombed and, minutes later, the owner strolls out with an extinguisher to deal with the everyday irritation. A tourist asks a policeman the way, and he produces a blindfolded prisoner from his van to supply directions. And, observing it all is a solitary figure, played by Suleiman, who has the good fortune to possess a remarkably cinegenic face and, with his sad, hooded eyes, looks like Buster Keaton's Arab cousin. Like Keaton, his humour is laced with melancholy. And he never, ever speaks.

"Not speaking is not a strategy. It's just not necessary," says Suleiman who, in person, is urbane, intellectual and, it turns out, enormously garrulous. "My cinema is a form of striptease and there comes a moment when it is essential for me to be in front of the camera. My character is definitely an extension of who I am. But I'm not the hero. I'm more like a spectator, asking questions."

Even so, Divine Intervention contains autobiographical elements. Two events triggered it: Suleiman's father (to whom the film is dedicated) fell seriously ill, and the director himself fell in love. In the story, his character watches his father's decline and makes constant trips to a bleak Israeli checkpoint to spend wordless trysts with his girlfriend who lives on the other side.

Suleiman, 42, was born in Nazareth, "a scary neighbourhood with a lot of violence which exploded suddenly; things were tense all the time." He dropped out of school at 15. "I became a street kid and that was quite an occupation for a while. Then I had to leave the country suddenly because a gang was being busted and I was held in the police records as its leader. Actually I'm a total coward."

He went to London. "I spoke English and was in a heavy metal band so I was fascinated with Led Zeppelin and British rock. I worked in a wine bar in Kensington for a few months." By the age of 21 he had moved on again and was an illegal immigrant in New York, "doing odd jobs, minimum wage stuff. I bumped into New York; I didn't really choose it." Still, he spent ten years there, on and off, devouring movies at random, often two or three a day.

At first he met no anti-Arab prejudice. "People thought I was from Pakistan. They had no notion then what Palestine meant." But things changed fast after the Gulf War, and Suleiman's first short, Introduction to the End of an Argument (1992), mocked Arab stereotypes in Western cinema, editing film clips into an satirical montage of "terrorists and oil sheiks." Another short, Homage by Assassination, reflected on the Gulf War. His debut feature, Chronicle of a Disappearance, was, like Divine Intervention, a series of comic tableaux of life in the Middle East mixing documentary and fiction. When it won the award for Best First Feature in Venice in 1996, both the director and Palestine itself were firmly on the map.

Suleiman builds up his films from small personal observations. "I keep notebooks where I write down things that tickle me, in the sense of making me laugh or provoking me." In one of Divine Intervention's most startling setpieces, a phalanx of Israeli gunmen aim at the painted target of a Palestinian woman who suddenly comes to life, deflecting bullets, Superwoman style. It was, Suleiman says, provoked by a detail which "tickled" him: a highway billboard outside Tel Aviv advertising a shooting range. Some viewers protested the apparent anti-Israeli violence. But he describes it as "Sergio Leone/Matrix kitsch – my character's fantasy, like Popeye opening a can of spinach".

Conversely, he was also attacked by Arabs for Chronicle of a Disappearance, whose last shot shows an Israeli flag. "They misread the irony of it and accused me of being a Zionist collaborator," Suleiman says with a shrug. Since he started winning more international recognition, including the Jury Award at Cannes last year, these voices have changed their tune. "Suddenly I'm their hero. Mr Arab Pride." But it looks as if he won't win a Foreign Language Film Oscar. In a decision which has caused further controversy, the American Academy has refused to consider Divine Intervention on the grounds that the Oscar is open only to countries recognised by the United Nations (Palestine is an "entity" with "observer status").

It's Suleiman's subtle, sceptical vision which needles his critics. But it is also what makes his work so intriguing. "I only put a scene in a film when I myself cannot comprehend it. When I come to understand what it means, I immediately chuck it away. There is no message in Divine Intervention. But I don't think it is an expression of despair.

"If I have a sensual moment of hands touching, or a gag that makes you laugh, that's already a kind of resistance. You can set up a checkpoint and ask for people's ID, but you cannot capture their imagination. I'm not claiming to be the poet of my time. But if you find a moment of truth in yourself that reaches other people, it becomes a magical communication which, maybe, can induce tolerance."

'Divine Intervention' (15) is out on Friday