“That critical moment we both knew would come someday – here it is…” After the jet-black social satire of Dogtooth, the role-playing bereavement of Alps and the quasi-sci-fi tragicomedy of The Lobster, Greek director Yorgos Lanthimos sets his sights on something altogether more unsettling. Segueing seamlessly from the theatre of absurdity to cruelty, he presents a tale of mythical, methodical revenge that starts with an ironic chuckle and moves inexorably towards a silent scream.

Taking its titular theme from the myth of Iphigenia, The Killing of a Sacred Deer is a wrathful tale of retribution and responsibility transposed from the stages of ancient Greece to the screens of 21st-century cinema. On one level it’s a typically arch dramatic conundrum, laced with Lanthimos’s trademark off-kilter artifice and deadpan humour. On another, it’s a Saw movie for the arthouse crowd, an increasingly sickening hunger game driven by an inflexible moral imperative, with a whiff of medical misadventure.

Colin Farrell, star of The Lobster, plays heart surgeon Steven Murphy – wealthy, slightly world-weary and too fond of a drink. An arresting opening image of a pulsating heart operation ends with surgical gloves being dumped in the trash, symbolically removing blood from the surgeon’s hands – for now. Steven lives in a grand, cavernous home with his wife, Anna (Nicole Kidman, Farrell’s co-star in The Beguiled), daughter Kim (Raffey Cassidy), and younger son Bob (Sunny Suljic). Their lives are materially rich, but emptiness prevails. Perhaps that’s what drives Steven to meet up with Martin (Barry Keoghan), a callow youth whose relationship with the surgeon is suspiciously unclear.

At times, Martin resembles a young Norman Bates, wide-eyed and unknowingly dangerous

For a while, things progress in familiar alienated fashion. The dialogue is theatrically mundane – discussions of watchstraps, lemon cake and menstruation, delivered in the monochromatic rhythms of a trance state. “General anaesthetic?” asks Anna, before draping herself across the bed in a comatose pose, feigning unconsciousness for her husband’s ritual pleasure.

Gradually, Martin inveigles his way into this picture-perfect family life, visiting the house, impressing the teenage daughter. Later, Steven meets Martin’s tragically needy mum (a sharp cameo by Alicia Silverstone), who tells him he has “beautiful hands”, and insists pathetically that “I won’t let you leave until you’ve tried my tart!” The line gets a giggle, but the laughter rings hollow. Slowly, what once seemed funny starts to become weirdly frightening.

Watch the trailer for The Killing of a Sacred Deer.

Lanthimos’s regular cinematographer, Thimios Bakatakis, accentuates the sense of dread as his cameras creep and crawl through hospital corridors, like the lurking spirits in The Shining – all low-angle prowls and ghostly high glides. Thunderous music cues (including bursts of Ligeti) crank up the cracked tone, ominous and screechy. As black comedy gives way to grand guignol, we are reminded of the tortured games that Michael Haneke once played upon his bourgeois protagonists and audiences. There are echoes, too, of The Exorcist as children succumb to mystery illnesses, leaving doctors pontificating pointlessly about psychosomatic symptoms in state-of-the-art hospitals.

Observing it all is Martin, brilliantly played by Keoghan to combine the awkwardness of youth with the suggestion of terrible power. At times, Martin resembles a young Norman Bates, wide-eyed and unknowingly dangerous. Elsewhere, he seems like a dorky descendant of Ezra Miller’s eponymous teen in We Need to Talk About Kevin, the bearer of projected parental guilt. Throughout, Lanthimos and regular co-writer Efthymis Filippou leave us tantalisingly uncertain as to whether this intense young man is the architect or messenger of forces beyond our ken. When awful truths are revealed, they are recited like cursed verse, conjuring a fable-like sense of fate, out of step with contemporary concepts of choice.

It’s that clash between the ancient and the modern, the farcical and the fearsome, which gives The Killing of a Sacred Deer its edge. While the setting may seem at first more “realistic” than the worlds of Lanthimos’s previous films, any sense of familiarity merely accentuates the eeriness of the otherworldly elements (Rosemary’s Baby author Ira Levin would have appreciated the juxtaposition). Similarly, the battle between ice-cool irony and full-blooded horror remains perpetually unresolved, leaving the audience squirming with uncertainty when things turn nasty.

Viewers will doubtless have their own vastly differing reactions to this bizarre drama. Farrell has said that making the film left him “fucking depressed”; others may be variously amused or appalled. I veered between being impressed, alarmed, confused and creeped-out. That, I suspect, would make Lanthimos laugh.