In previous films, Michael Haneke has shown a ruthless fascination with cruelties that people are capable of inflicting on one another. They are quietly imposed, like the video voyeur of “Cache,” or appalling as child abusers in “The White Ribbon” and the home invasion violence of “Funny Games,” a movie Haneke remade in English to share the nihilism with more viewers, convincing me he’s as callous as those intruders are with victims.

Haneke is typically unflinching with “Amour’s” story, denying any sentimentality or hope for an uplifting resolution. That the movie ends in death is obvious from the beginning, when policemen break down the door of the apartment and discover a withering corpse inside. Yet this is a movie of profound insight and compassion that, although muted, is more than I expected from Haneke. “Amour” is depressing only if you immediately dismiss it.

We meet Georges (Jean-Louis Trintignant) and Anne (Emmanuelle Riva) in her final evening of lucidity, a cultured couple attending a piano concert. That night Anne has trouble sleeping. The next morning she has trouble responding to Georges’ conversation, the result of a stroke. After hospitalization she returns home, her speech and mobility paralyzed. Anne will never leave the apartment alive again.

“Amour” proceeds at a funereal pace, with Anne’s condition worsening and Georges’ emotional endurance fading. This is a movie almost too painful to watch at times, yet so masterfully composed and acted that it’s impossible to turn away. Nothing about the title is ironic as I feared from Haneke; “Amour” is a somber, affecting exhibition of “love” in its most challenged state, after hope evaporates and nothing remains except memories.

Only in “Amour’s” final minutes does anything perplexing occur that approaches Haneke’s earlier works. The filmmaker’s newfound sense of mercy still may be interpreted as cruel.

As usual, Haneke doesn’t care what viewers think, only that they feel.