CANNES, France >> It’s taken a lot of time and a good deal of yearning for Australian director George Miller to make “Three Thousand Years of Longing, ” his long-awaited follow-up to “Mad Max: Fury Road.”

Miller premiered “Three Thousand Years of Longing” over the weekend at the Cannes Film Festival, the culmination of a journey that began 20 years ago when Miller first read the A. S. Byatt story upon which the film is based, “The Djinn in the Nightingale’s Eye.”

But it was only when frictions over the profits from “Fury Road” — Miller’s operatic action opus — opened a window that the time came for “Three Thousand Years of Longing.”

“After we wrote it, it was really a question of when to do it,” Miller said alongside his stars, Idris Elba and Tilda Swinton, shortly before the film’s premiere in Cannes. “It was lucky, actually. We got into litigation with Warner Bros. on ‘Fury Road’ and it meant that, hey, we can bring this to the fore.”

The unveiling of “Three Thousand Years of Longing” had most Cannes festivalgoers on the edge of theirs seats. What would Miller conjure up this time? Could the 77-year-old filmmaker match the propulsive thrill of “Mad Max: Fury Road”?

That film, which Miller is preparing to revisit with the prequel “Furiosa,” made its blistering premiere in Cannes seven years ago on its way to an armful of Oscars, $374 million in box office receipts and a place on plenty of best-century lists.

The answer, it turns out, is a singular blend of fantasy epic and chamber-piece drama that goes to the heart of Miller’s own feelings about storytelling. The film, which MGM will release on Aug. 31, was scripted by Miller and his daughter, first-time screenwriter Augusta Gore. In it, Swinton plays a narratologist named Alithea Binnie who is visiting Turkey for a conference on how science has replaced mythology.

After Alithea buys an old bottle at the Grand Bazaar and scrubs it in her hotel sink, a wish-granting djinn (Elba) appears, filling up the room. A lengthy and intimate conversation ensues, in which he tells her about his previous masters throughout the last 3,000 years. Using computer-generated imagery, Miller blends mythology and modern world in a contemplative, history-spanning fairy tale that resolutely believes in magic.

“There are some people who are great storytellers, who can do it as a performance,” Miller says. “I know that I struggle with that. I can’t get up and tell a spontaneous story well. But I can do it in the ultra-slow motion of telling a movie, where I think about every nuance, every rhythm of it.”

Miller teamed up again with many of his “Fury Road” collaborators, including cinematographer John Seale, editor Margaret Sixel and composer Tom Holkenborg. But the director sensed that in some ways “Three Thousand Years of Longing” was the “anti-Mad Max” — talkative where “Fury Road” was wordless, spread across eons rather than in real time.

Reactions have been mixed to “Three Thousand Years of Longing,” but few have questioned its ambition or its uniqueness.

And for all the eras it spans, the movie reaches right up to today. The pandemic is seen late in the film in scenes where background actors are wearing masks. The film’s production was also dramatically shaped by the pandemic. Miller shifted from shooting in a series of international locations to relying on CGI and his native Australia for the bulk of the film.

“When we started talking about this film, it felt very right,” Swinton says. “But now, this year, it’s even more. And I imagine it will be even more the next. That instinct of yours for on the wind, that’s going to run and run. That’s like a seed that one plants.”

To Miller, “Three Thousand Years of Longing” doesn’t just lead up to now — it goes beyond.

“It’s a very pertinent story,” says Miller. “It’s like a metal detector or a Geiger counter, when something really activates it. You go: ‘Oh, there’s a rich seam in here somewhere.’”

“Time will tell if it has enough stuff going in it that other people respond to it. You hope that the story becomes someone else’s and belongs to everyone,” he said.