The Anglo-Irish writer and director John Michael McDonagh opens his cold, mordantly funny murder mystery, “Calvary,” with a misleadingly pacific image: a close-up of the Irish actor Brendan Gleeson. An imposingly big man who’s often called on to suggest authority, Mr. Gleeson has played cops, criminals and Winston Churchill, and had the recurring role of Mad-Eye Moody in the Harry Potter series. In “Calvary,” he plays a world- and time-tested expert of another sort: Father James, a conscientious priest and widower whose faith isn’t shared by his flock, which includes a serial sinner, a hostile Buddhist, a dog hater and other furious souls, including one self-professed future executioner.

The killer makes his entrance right after Father James, seated off screen in a confessional and issuing convincing threats. This seeming penitent, or rather Mr. McDonagh, makes his intentions immediately clear: The confessor has singled out Father James, whom he calls a good priest, to take the fall for the sins of the Roman Catholic Church and its bad priests. “I’m going to kill you because you’re innocent,” the confessor promises, words that — with the title — seem to tip Mr. McDonagh’s hand. Calvary is the name of the Jerusalem hill on which Jesus is said to have been crucified; the would-be murderer prefers a more level playing field: He tells Father James to meet him in a week on the wildly beautiful, wind-swept beach that hugs this provincial Irish hell.

Mr. McDonagh returns repeatedly to the beach and the rolling hills flanking it, beginning with the soaring opening aerial shots, images that are known as bird’s-eye or, more fittingly here, God’s-eye views. (The director of photography, Larry Smith, also shot Mr. McDonagh’s first feature, “The Guard.”) The stark, natural landscapes are among the movie’s most seductive attractions, even if the characters populating them seem calculated for maximum repulsion. There’s the butcher and possible wife beater, Jack (Chris O’Dowd), who may take a fist to his missis, Veronica (Orla O’Rourke), but doesn’t seem terribly put out that she’s carrying on with a mechanic, Simon (Isaach de Bankolé). There’s also a dying writer, Gerald (M. Emmet Walsh), and a dyspeptic surgeon, Frank (Aidan Gillen).