Imeet Peter Greenaway in the Rembrandt room of Amsterdam’s Rijksmuseum, where there is a fairly chaotic queue waiting to see what the controversial British film director has done to one of the most famous paintings in the world. The fourth most famous, Greenaway specifies with characteristic precision, after the Mona Lisa, the Sistine Chapel ceiling and “The Last Supper”. He is talking about “The Night Watch”, Rembrandt’s moody scene of mysteries unsolved and miraculous lighting effects that might have been designed to appeal to the maverick filmmaker’s refined and quizzical sensibilities.

Greenaway has created a theatrical installation that dares to play with the surface of the painting itself. The lights go down, visitors take their seats in a mini-theatre and the painting comes to life: dogs bark, bystanders chatter, the rain lashes down: all of these suggested by a vivid soundtrack and the play of lights on the painting. The piece lasts only a few minutes but it is captivating, and at the end there is applause.

“It’s not a painting, it’s a drama – people clap!” Greenaway says with rare glee as we sit for coffee afterwards. I say it is an entirely new way of looking at familiar art works. That was the intention, he replies. “What did Picasso say? The worst thing you can do to a painting is to put it on a wall, because within three days everyone will have forgotten it. Perhaps part of the brief here is to make people look at the bloody thing.”

But it would be untypical of the cerebral Greenaway to be content with producing an upmarket son et lumière for summer tourists. Part of the appeal of “The Night Watch” is its air of secrecy. What exactly is happening? Who is the mysterious child, lit so prominently next to the painting’s protagonists? And the musket shot, whose flame is scarcely visible behind the yellow hat on the right: what is that all about?

Greenaway has a theory. It is inevitably complicated, revolving around the visit to the Netherlands of Mary Stuart in order to barter the crown jewels on behalf of her father Charles I, and a feud between the militiamen entrusted to meet the young princess. The feud resolved itself in a faked military accident, planned by Frans Banning Cocq, the central figure in Rembrandt’s painting. Rembrandt was already in a feud himself with Banning Cocq’s brother-in-law, who had refused to pay for an unflattering portrait.

“The Night Watch” is the painter’s coded commentary on the entire incident, full of obscure visual references that must, to Greenaway, mean something: why does the shadow of Banning Cocq’s hand obviously grope his companion’s belly and genitals? Does it speak of a hidden sexual affair? And why is there a right-handed glove in his hand when it is his left hand that is ungloved? Is some kind of gauntlet being thrown? And the girl, Mareike – a dwarfish reference to Velázquez and by extension Spain, the enemy?

I ask Greenaway what appealed about the project and he takes off on a fluent, erudite and uninterruptible narrative that largely amounts to an abiding admiration for the painter, and his own well-chronicled love of mysteries. “Rembrandt fits all the things we think we ought to think about: he is deeply humanist, republican, democratic, pro-proletarian, very ironic, and postmodernist. The so-called man in the street has a comprehension of what he is about: he paints old people, babies in diapers, the ugly woman next door. A post-post-post-kitchen sink romantic.” I wonder what that means, but there is no time to think, let alone ask.

“And the way he starts in the dark and moves towards the light, the way cinema does. If, as Godard says, cinema is truth at 24 frames a second, this is a nanosecond. It feels like a frozen frame from a movie. Rembrandt, and other great masters of the Baroque, were inventing the language of cinema.”

We cut to the chase. It was cinema that thrust Greenaway into prominence in the 1980s, with a succession of art-house hits such as The Draughtsman’s Contract and The Cook, The Thief, His Wife and Her Lover, but he has never hidden his more exalted love affair with painting (“I still don’t feel like a film director, more as a painter manqué”) which itself became the theme of some of his complex narratives. Today his disenchantment is complete: he pronounces cinema dead, while arguing vigorously for the continued relevance of painting.

“You know [Jacques] Derrida said the image always has the last word, which is very witty, but doesn’t go far enough, because the word itself is an image. A painting is for all time. Cinema has been going for 111 years, which is not a very long time, and I feel it has exhausted itself. When you see a movie now, within five minutes you know what is going to happen, how it will turn out: you understand the genre.”

That may be true of mainstream Hollywood, I say, but what about, I don’t know, Iranian cinema?

“But it still follows the tropes and the paradigms,” he says resignedly. “This new stuff: oriental, exotic Antonioni, the inner man, basically nothing happening but everything happening, God working in small things: we have seen it all before, haven’t we? Haven’t we? Haven’t we?”

There is almost an edge of desperation here, like the insistence that one is over a former lover. Presumably he didn’t feel like that when he started his film career?

“When I started out, there were about a dozen great directors making completely different types of movies. The Italian cinema was alive and thriving. The nouvelle vague and Godard, who was such an influence on us all.”

But Godard was already proclaiming the death of cinema in the 1960s.

“He threw it all away. If you are European, Eisenstein invents cinema, Fellini consolidates it, Godard throws it all away. But that’s all right. There are new forms of technology, new ways of making things.”

I remind Greenaway, as if he needs reminding, that this kind of talk – unashamedly led by complex ideas, epic in range, littered with quotes from Godard and Derrida – does not go down terribly well in British circles, and I can’t help noticing that he has lived in Amsterdam for 12 years.

“They are so Protestant, so puritanical,” he says slightly pityingly of his compatriots. “But I don’t want to make it sound like a political gesture,” he says of his move. “It was an attraction away rather than a retraction from.”

We talk a little about his ongoing film project, The Tulse Luper Suitcases, which he describes as “92 stories about Holocaust gold”. It is seven hours long, he says, and he is working on the DVD version. He adds, with a pride that is curiously touching, that he has written a book about suitcase number 46, and that it has just been translated into Russian. He describes his approach as encyclopaedic, and says he doesn’t like “looking for closures”.

This seemed a long way from the cinematic mainstream. Isn’t he tempted ever to retur ever to return to its comforting fold? He shakes his head. “I was fortunate to meet a Dutch producer who said that, provided I didn’t employ Elizabeth Taylor or an American aircraft carrier, he would be happy to support my future film career. We have made 12 feature films and 50 other films. But we are not rich. I don’t drive fast cars or live in yachts in Cannes.”

His films are often described as cold and unsentimental.

“Yes.”

Why is that?

“Think of the subject matter.”

I say they are all about sex and death.

“They are savage pieces of extreme black humour. I come from the same place as Monty Python. When Michael Gambon first saw his performance in The Cook, The thief, His Wife and Her Lover he laughed all the way through it. I thought: ‘You have got it!’”

I say the scene in that film where a character was suffocated by being forced to eat paper made me feel physically sick.

“You’re a writer – that’s a nice idea, being killed by your own writing. Isn’t it a nice idea?

I pass. “[Quentin] Tarantino commits huge atrocities of sex and violence, why doesn’t he get any flak? Why do I get all the flak? I think I know the answer. He does it for a giggle. For a frisson. He lets you off the hook. But you have to have that sense of responsibility. If you are going to do sex and violence, whoa, watch out. Because there are huge recriminations.”

We have come to the end of our coffees, and Greenaway talks about future projects – a play and film about Rembrandt, who is played in the latter by The Office’s Martin Freeman, and several prospective acts of non-narrative non-closures. But as we turn towards the museum he takes on an almost wistful air and says: “I don’t think anything can top this.”

‘Nightwatching’ by Peter Greenaway is at the Rijksmuseum, Amsterdam,  tel +31 20 6747047, until August 6