It’s a tale as old as the pulps: a hit-man, old, world-weary and ill, suddenly finds himself both falling in love and threatened by his own colleagues in the trade. That’s the clichéd plot of “Asher,” which is nonetheless distinguished by a couple of factors.

One is that the protagonist is not a member of the traditional Mafia, but of a New York Jewish crime cabal apparently staffed, at least in some measure, by former members of the Israeli intelligence services. The other is that he’s played by Ron Perlman, the beefy, granite-faced actor who, apart from roles like the television-series Beast (as in “Beauty and…”) and “Hellboy,” in which he wore heavy makeup, has generally been limited to secondary roles.

Perlman brings a gruff dignity to the title character, who lives a solitary life, making fine meals for himself that he eats on his apartment balcony, while handling the assignments given him by his handler Abram (Ned Eisenberg), a dry-cleaning store proprietor. Though he’s occasionally partnered with a helpful hooker (Marta Milans) who lures victims in for the kill, Asher usually works alone, and has a standard operating procedure: he sets off the smoke detector in front of a target’s apartment door with a cigarette (protecting himself with the umbrella he always carries on a job), and shoots the man as he rushes out into the hall.

Asher is, however, unwell, suffering from a bad ticker (literally as well as figuratively), and when trying to take out one of three targets assigned him directly by gang boss Avi (Richard Dreyfuss)—intended as revenge for the killing of a colleague and his family by a rival outfit—Asher collapses at the door of Sophie (Famke Janssen), a ballet instructor who revives him. He takes a liking to her and returns to invite her to dinner; unlikely romance blossoms.

But Sophie also has a cross to bear—taking care of her elderly mother Dora (Jacqueline Bisset), who’s suffering from dementia. That allows scripter Jay Zaretsky to pen some heavy-handed conversations between her and Asher about the morality of taking another person’s life, instigated by Dora’s request that her daughter end her suffering.

Asher’s professional responsibilities intervene, however, when he’s ordered to join Uzi (Peter Facinelli), a younger member of the gang whom he’d once mentored, and his crew in a mission as a sniper. Unfortunately at the crucial moment he suffers a seizure, and the job is nearly bungled. That makes him a target of his colleagues, and Sophie is put in danger in the process; resolving the matter will force Asher to extreme measures.

Director Michael Caton-Jones handles this material—not his specialty—reasonably well, though he establishes a very deliberate pace and was clearly hampered by a modest budget (an unconvincing explosion at one point indicates that the effects team didn’t have many resources at their disposal). But except for Dreyfuss, who goes very hard on the shtick, the cast maintain a restrained, serious approach, with Janssen more affecting than she has been in some time and Bisset convincingly conveying Dora’s cantankerousness.

The picture really belongs to Perlman, though, and his broad shoulders prove capable of carrying it, even if Asher is basically a stock figure. The familiarity of its over-the-hill hit-man plot leaves “Asher” of cable or streaming-service quality, but Perlman’s formidable presence makes it watchable on those secondary venues.