“The Killing of a Sacred Deer” is a horror film. It’s also a black comedy, a family drama and a peculiar evocation of the Iphigenia myth.

For much of the film, it’s hard to understand why its characters are acting as they do, and even when the picture finally starts to come into focus, the film operates on an internal logic that’s divorced from real-world circumstances. The opening scene is a conversation about wristwatches that turns into a running gag of sorts, with divergent opinions over the utility and style of metal versus leather bands. In a word, the film is “weird,” misbehaving in ways that deliberately confound the expectations of audiences used to getting all the information up front.

The director, Yorgos Lanthimos, has a gift for turning disorientation into a narrative weapon. His breakthrough feature, “Dogtooth,” confines three young adults to a remote country estate that they can never leave, quarantined by parents who have taught them a made-up language (“zombies,” for example, are a word for little yellow flowers) and invented a fourth sibling whose terrible fate is held up as a cautionary tale. It’s a brilliant parable for isolationism and how the powerful withhold truth and knowledge to build up barriers.

More recently, Lanthimos made his English-language debut with the cult hit “The Lobster,” a science-fiction comedy about a dystopian hotel where single people are given 45 days to find a romantic partner or get turned into the animal of their choice. There’s no indication of where or why this hotel exists, just as there’s no indication of why the children of “Dogtooth” are penned into the family estate. As with “Killing of a Sacred Deer,” Lanthimos would rather leave questions hanging in the air, while engaging viewers with a wicked sense of humor and a bold cinematic style that lands somewhere between the clinical precision of Stanley Kubrick and the prankish malevolence of Lars von Trier.

Speaking from his hotel at the Toronto International Film Festival, where “The Killing of a Sacred Deer” was making its North American premiere, Lanthimos says his way of making films simply reflects his interests as a moviegoer. “It’s much more intriguing and rewarding if I watch something and I’m engaged in an active way,” he says, “and not just presented with a very specific reality and told what I must think and what I must feel. I don’t have the answers, and it allows people to have their thoughts and opinions about certain things.”

Not knowing all the information upfront is also human nature. We keep secrets from each other and from ourselves, and “The Killing of a Sacred Deer” is about a whopper of a secret that threatens a well-to-do family. Colin Farrell, who had the lead role in “The Lobster,” this time plays Steven Murphy, a wealthy, accomplished cardiovascular surgeon who reaches out to Martin, a curious and disturbed teenager (Barry Keoghan), and takes him under his wing. Lanthimos and his co-screenwriter, Efthymis Filippou, hold off on revealing why Steven is fostering a relationship with the kid, but he nonetheless feels compelled to introduce Martin to his wife (Nicole Kidman) and two adolescent children (Raffey Cassidy and Sunny Suljic). Needless to say, this decision is regrettable.

Asked about what’s motivating Steven to befriend Martin and bring him into his home, not even Farrell has a clear answer. Speaking by phone after the festival, Farrell suggests that he didn’t need to know Steven’s motives any better than the character knows himself. “I’m not really sure if he’s operating from a place of guilt,” Farrell says, “or just trying to maintain his own personal and professional status quo.”

Farrell points to two different exchanges in the film, one in which Steven claims that “a surgeon can’t be responsible for a patient’s death, [but] an anesthesiologist can.” Later, the anesthesiologist (Bill Camp) says the precise opposite. “You have all these people who are so cluelessly washing their hands of any culpability or responsibility, as people tend to in life. I think Steven’s arrogance and desire for self-preservation — for [maintaining] what he deems the ideal American Dream life — is something so keen in him that I’m not sure if guilt appears on the radar.”

“The Killing of a Sacred Deer” won the best screenplay award at the Cannes Film Festival in May, but it isn’t the type of film that’s destined for universal approval. Between its elusive plotting, the escalating unpleasantness of Martin’s presence in Steven’s life, and a wrenching decision that has to be made on the children’s behalf, the film is more interested in challenging viewers than courting them. As with Lanthimos’s other work, it tends to draw strong reaction on both sides of the critical divide.

“If you’re making the kind of films I’m making,” says Lanthimos, “you kind of understand that not everybody can like it.”

“I prefer that they’re divisive,” he adds, “because I know there’s so many people with different tastes and [who] are used to different things that I would never want my films to be.”

“Hey, if you can give me film scripts that’ll be guaranteed to be liked, I might just call it a day and sign up for every single one of them,” Farrell jokes. “How you make a film that’s good, I don’t even know. Some people find [Lanthimos’s] work very entertaining, and some people find it maddeningly provoking. I just know, as an actor, to repeat myself is the dullest thing I could possibly do.” As for continuing their collaboration, Farrell says, “If I could work with him once every few years for the rest of my life, I probably would,” although he does add a note of caution.

“I don’t think I’d like to make two Yorgos films in one year. That would finish me off. I say that with absolute affection and admiration for how deep the stuff goes in. In ‘The Lobster’ but particularly on ‘Sacred Deer,’ by the end of [production], even though I know it’s all make-believe, I have to say I was pretty depressed.”