Abderrahmane Sissako’s “Timbuktu” is as far removed from Jacques Tourneur’s 1959 film of the same name as could be imagined. The earlier picture was a piece of ludicrous adventure hokum starring Victor Mature and an imposing hat his character always wore. Sissako’s is a piercingly relevant study of life under the rule of Islamic jihadists.

The film is set, as the title indicates, in the fabled city that was once a major hub along the medieval African trade route and a byword for a remote, exotic locale. The time is 2012, when the now-impoverished backwater town had been taken over by the militant Islamist group Ansar Dine as part of its conquest of northern Mali. (French and Malian troops retook it in 2013.) The opening scenes portray the brusqueness of the gun-toting militants in dealing with the remaining local population (many had fled, of course), as they bark out directives designed to impose conformity with their idea of Sharia law—women must be veiled and wear socks and gloves, soccer is forbidden, and so are music and smoking. They also systematically destroy cultural artifacts like masks and wooden statues, which they mow down with automatic weapons.

But the picture isn’t a documentary—it was shot not in Timbuktu but in Mauritania, and integrates an array of credible fictional characters within the recreated historical setting. Among them are the jihadists, led by a man who has no answer when the saintly local imam (Adel Mahmoud Cherif) demands to know where God is in his sternness, and who justifies his support of one of his men who has forced a young woman to marry him despite her family’s opposition with the simple proposition that his interpretation of the law is ipso facto the correct one. (He describes his group simply as “the guardians of all deeds,” a rather inclusive description.) Abdelkrim (Abel Jafri), another of the militants, not only sneaks out regularly to smoke, despite the prohibition—indeed, his driver points out that everybody knows he’s doing so—but shows an unseemly attention to Satima (Toulou Kiki), whom he orders to cover her head but is obviously interested in for other, less religious reasons.

Satima is one of the locals who suffering absurd, often brutal treatment at the hands of the jihadists, who are portrayed as thugs often clueless about the very faith they claim to be representing and incapable of dealing with ironic resistance (local boys, for example, get around the prohibition on soccer by ostentatiously playing in mime form, without a ball). She’s the wife of Kidane (Ibrahim Ahmed), living with him and their daughter Toya (Layla Walet Mohamed) in a spacious tent outside town, where he lounges strumming on a guitar while orphan Issan (Mehdi AG Mohamed) tends to their eight head of cattle. It’s this little family that becomes the focus of the film’s most extended episode of jihadist “justice.” Kidane has a running feud with a local fisherman, a surly sort who orders Issan to keep the cows away from his nets. When one of the animals wanders off into the river, the fisherman kills it, leading Kidane to confront the man with a gun—with a fatal result. A court conducted by the militants hands down a demands for compensation or “blood money”—forty cows—which Kidane cannot possibly pay, and so he is sentenced to death.

But Kidane is not the only one to be so summarily dealt with. A woman (Fatoumata Diawara) arrested for singing is sentenced to forty lashes, and the films observes the punishment with sad restraint rather than obvious indignation. An adulterous couple is buried to the neck and then stoned, though again Sissako stages the gruesome event with discretion, showing only its beginning and then cutting away. Other episodes center on minor infractions, as when a fish-seller is hauled off for protesting the demand that she put on gloves. But there is the occasional dissident who escapes the militants’ supposed justice, most notably the colorfully-garbed Zabou (Kettly Noel), an eccentric whose wildly dismissive attitude in the face of such inhumanity is ignored, probably because she’s thought to be mad.

Sissako’s treatment of all these vignettes shows a mastery of tone that’s complemented by the luminous cinematography of Sofiane El Fani; together director and cameraman create a series of unforgettable images, like the long shot of Kidane slowly walking to the shore of the river after his fatal confrontation with the fisherman. Composer Amine Bouhafa adds to the film’s spell as well, as does editor Nadia Ben Rachid, whose unhurried approach allows the work of the ensemble cast to breathe without rushing.

“Timbuktu” is a wrenching portrait of peaceful people suffering under the rule of self-righteous, unthinking fundamentalism, presented in a powerful neorealist style.