Greek director Yorgos Lanthimos has been responsible for some of the most provocative and peculiar films of the past decade. His Oscar-nominated movie “Dogtooth” (2009) depicted a married couple who had kept their grown-up children confined at home for their entire lives. “The Lobster” (2015) — his first film in English, and an unlikely cult hit — was set in a world in which coupledom is legally mandated, and those who can’t find a romantic partner are transformed into animals.

Lanthimos’ latest feature, “The Killing of a Sacred Deer,” opens with a graphic depiction of open-heart surgery, but that’s just an appetizer for the portentous drama that follows. Loosely inspired by the Euripides tragedy “Iphigenia in Aulis,” it tells of a successful surgeon (Colin Farrell) who finds himself forced to atone for the death of a patient in the grimmest of fashions: by choosing to sacrifice a member of his own family.

Yet describing the premises of Lanthimos’ movies doesn’t fully capture the unsettling quality they possess. They hover between comedy, surrealism and nihilistic drama, all delivered with a deadpan restraint that makes their intentions harder to parse.

“There’s a certain tone and some kind of philosophy of how I approach things and how I do things,” he says, speaking by phone from his home in London. “But I think and I hope that there’s some differentiation between the films.”

If “The Lobster” was almost cute — scenes of torture and self-mutilation notwithstanding — “The Killing of a Sacred Deer” opts for full-blown Gothic psychodrama. The prowling camerawork and avant-garde classical soundtrack (including Sofia Gubaidulina and Stanley Kubrick favorite Gyorgy Ligeti) conjure an atmosphere of dread that’s so enveloping, it’s easy to overlook the film’s lighter elements.

There are laughs to be had along the way, albeit of the cringing kind: Farrell’s character casually mentions during a cocktail party that his daughter has just started menstruating; his wife (Nicole Kidman) spices up their sex life by pretending to be anesthetized in bed; and Barry Keoghan, as the doctor’s glass-eyed teenage nemesis, delivers one of the most indelible screen depictions of spaghetti-eating since “Lady and the Tramp.”

Does Lanthimos think of the film as a comedy?

“Not really, no,” he says, chuckling. “I just think that it has humorous elements and situations. It kind of tries to blur the lines between what’s horrific and what’s ridiculous and what’s funny — and, I guess, put people in an awkward position sometimes to figure out for themselves whether something is funny.”

This is part of what makes Lanthimos’ brand of cinema so confounding, and divisive. He’s normally reluctant to discuss what his films actually mean, which might explain why some critics have been quick to dismiss them as empty. But when I mention that I found “The Killing of a Sacred Deer” funnier — and a lot less traumatic — on the second viewing, he sounds pleased.

“That’s great,” he says, “because if a film is complex enough to be able to be seen from the same person in different ways, imagine how different it can be for different people from different cultures and different backgrounds and educations — all of those things.

“It’s so complex that you can never really fine-tune the work you make in order to have a very specific effect to everyone,” he continues. “It’s always a ballpark. You aim for something, and you hope enough people are going to experience it in a way that you kind of thought that they would.”

“The Killing of a Sacred Deer” is the fourth film that he has written with Efthymis Filippou (their previous collaboration, on “The Lobster,” earned them an Oscar nomination), and the script preserves the curious cadences that have become one of the defining traits of their work. The dialogue tends to be flat and expository, and actors deliver it in a stiff monotone; even in his most emotionally intense scenes, Farrell could pass for a mildly peeved bureaucrat.

“The sound is quite important for me, and the language and the tone,” Lanthimos says. “I think the script has a very specific tone, so it does sound wrong when you change things — at least to my ear.”

His directorial style is similarly exacting. Speaking at a press conference at last year’s Cannes Film Festival, where the film screened in competition, Kidman said Lanthimos’ typical approach was to tell actors: “Please do nothing.”

“I think it’s a difficult thing to ask in general, and quite vague in a way,” Lanthimos explains. “It’s really hard for actors to be present and subtle without thinking that they’re not doing enough, and that they’re not projecting enough, and that they’re not portraying the characters that they have to portray in the best way possible. There’s a conflict and fight within themselves, mostly, and I’m there to just encourage them to go with it.”

The resulting effect is perhaps more comparable to absurdist theater — think Harold Pinter or Eugene Ionesco — than the conventional methods of arthouse cinema.

“People are used to a certain type of acting and a certain type of tone,” Lanthimos says, “and they quickly reduce something like this to ‘monotone’ or ‘monochromatic’ or whatever.”

It’ll be interesting to see how he fares in his next film, “The Favourite,” which is due for release later this year. It’s an 18th century costume drama for starters, and sees Lanthimos working from someone else’s screenplay for a change. However, his distinctive voice seems likely to emerge intact.

“I always felt that I needed to be in control of the project that I develop or make into a film,” he says. “I don’t think it would be easy for me to work in an environment where I would be just hired as a director.”

“The Killing of a Sacred Deer” opens in cinemas nationwide on March 3. For more information, visit www.finefilms.co.jp/deer.

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