There have been a number of great films about the Italian—or Sicilian—Mafia, most notably the first two “Godfather” pictures, but until now the Russian mob hasn’t gotten its cinematic due. David Cronenberg changes that with “Eastern Promises,” a riveting drama that adds a potent familial layer to a tale of twisted gangland schemes—and boasts a sequence of an attempted assassination in a steambath that’s as brutally brilliant an exhibition of cinematic craft as the staircase rape scene was in “A History of Violence.” (You might also compare it to the shower scene in “Psycho.”) Cronenberg is truly the master of the moment as well as the whole. “Promises” doesn’t strike me as being quite as impressive as “Violence,” whose juggling of tones was nearly miraculous: it’s more conventionally excellent rather than strikingly new, as the earlier film was. But it’s only by comparison to Cronenberg’s best that it comes up slightly short.

The picture, sharply written by Steve Knight (who penned Stephen Frears’ superb “Dirty Pretty Things”), opens with two deaths in different London locales: the first of a Russian gangster viciously killed while getting a haircut, and the second of a young woman who expires on an operating table while giving birth to a daughter. The script proceeds to tie these two events together through a long and canny chain of connections that culminate in revelations about the workings of the Russian mafia and the complicated relationships within its leadership. The main characters include Anna (Naomi Watts), the midwife who helps deliver the woman’s baby and, having recently suffered a miscarriage herself, is concerned about finding the child’s family; Semyon (Armin Mueller-Stahl), the soft-spoken but slightly sinister owner of the genteel Trans-Siberian Restaurant, whom Anna asks for help in translating the deceased’s diary, in which a card advertising his place was inserted; Semyon’s loose cannon son Kirill (Vincent Cassel), who has too great a fondness for booze and hookers; and Kirill’s driver Nikolai (Viggo Mortensen), a coolly efficient, utterly self-composed man with a strangely gentlemanly air. Others circling around them include Anna’s concerned mother Helen (Sinead Cusack) and her cynical brother-in-law Stepan (Jerzy Skolimowski), who claims to have been a member of the KGB and warns his niece that her inquiries might be very dangerous.

Too many hints about how everything and everyone come together in this snugly-constructed film would be unfair; suffice it to say that it has plenty of twists and surprises along the way to a satisfying conclusion that isn’t pushed too far. And the fact that it isn’t is attributable to Cronenberg’s approach, which as usual with this director is cerebral rather than emotional. That’s not just true of the way in which the film is shot and constructed and scored (by cinematographer Peter Suschitzky, editor Ronald Sanders, and composer Howard Shore—longtime Cronenberg associates), but the tone in which the story is told. Cronenberg is, in his way, as seemingly dispassionate in his presentation of the tale as Nikolai is in fulfilling his duties within it. That’s deceptive, of course, because the chilly, almost automatic efficiency actually screws up the tension as effectively as a more florid approach might. In other words, the Coppola approach worked well, but so does Cronenberg’s leaner, meaner one.

But the writer and director and behind-the-camera contributors aren’t the only heroes of “Eastern Promises.” So are the cast. Watts doesn’t dominate the proceedings but is quietly moving throughout, and the same can be said of Cusack on a smaller scale. Cassel comes on a bit too strong as the wild-eye Kirill, and Skolimowski is unrestrained too, though in his case the faintly comic result comes across as entirely appropriate. But it’s Mueller-Stahl who’s most impressive among the supporting players, combining courtliness and menace with consummate ease.

Even he pales, however, beside Mortensen. This is his picture as much as it’s Cronenberg’s. He’s long been considered a good journeyman actor, but under the director’s astute guidance he’s blossomed into a remarkable leading man, first in “Violence” and now here. In his hands Nikolai is a man of extraordinary control, and the actor shows he is, too. Given that bathhouse scene, this is a brave turn; but there and elsewhere it’s also a simply mesmerizing one.

So what “Eastern Promises” offers is a great performance in a film that, by Cronenberg’s highest standards (“Dead Ringers,” “Spider,” “Violence”) is a mite below his best. But a film slightly below Cronenberg’s best is still leagues ahead of the best that most other directors have to offer.