The sequel to Denis Villeneuve’s exceptional 2015 “Sicario,” about drug trafficking at the US-Mexican border, subtitled “Day of the Soldado,” is, like its predecessor, a tough, gritty crime drama, this time focusing on human trafficking in the same locale. Though Emily Blunt has left the cast, Josh Brolin and Benicio Del Toro have returned, and though Villeneuve has departed as well, Stefano Sollima proves a more than capable replacement.

Most importantly, perhaps, Taylor Sheridan is again the screenwriter, and he peppers the script with sharp dialogue and plenty of opportunities for the violent action that marked the first film. Yet there are two narrative problems with his work. One is that the basic turn in the tale’s last act hinges on an unlikely coincidence that joins two story threads together. The second is that the movie ends inconclusively, leaving the audience hanging. Presumably that’s to pave the way for another installment in the series, but while mega-franchises can get away with that, whether “Sicario” has enough brand loyalty to do so is questionable.

Those are considerable impediments for any film to overcome, and the fact that “Soldado” manages the trick as effectively as it does is a tribute to the skills of Sheridan, Sollima and the cast and crew.

The film begins with gruff black ops veteran Matt Graver (Josh Brolin) using extreme methods to get a Somali pirate to talk about how terrorists were smuggled into the U.S. to blow up a Kansas City megastore; it’s suggested that their route was across the Mexican border, where drug cartels are now making enormous profits in human trafficking.

In response, Graver is informed by the Secretary of Defense (Matthew Modine) that the President has decided to treat the cartels as terrorist organizations, and thus targets to be attacked at all costs. Graver suggests that the best route would be to get them involved in a war against one another, which could be prompted by the abduction of Isabela (Isabela Moner), the twelve-year old daughter of Carlos Reyes, the head of the most prominent cartel, which could plausibly be blamed on his rivals. She is taken as planned, and then supposedly freed by a phony DEA raid on the Texas house where she is being held.

The intention is to turn the girl over to Mexican authorities for safekeeping, but of course the plan goes awry, since no one can be trusted; the result is that a bunch of Mexican federales are killed, and Isabela is left stranded in the desert with only Alejandro (Del Toro), the erstwhile sicario turned occasional U.S, agent, to protect her from her father’s many enemies. The debacle has also led the wimpy President and his Defense Secretary to end the mission and order all evidence of it to be scrubbed clean, a message delivered to Graver by a CIA apparatchik (Catherine Keener).

While all this has been playing out, the script periodically inserts episodes in the recruitment of McAllen, Texas teen Miguel (Elijah Rodriguez) by cartel underlings to serve as a coyote leading illegals across the Rio Grande. Eventually this narrative thread dovetails with the larger plot to lead into a twisty final act, as well as a coda designed to invite another installment. Unfortunately, the way in which Sheridan has devised the connection, and the rather overstated way in which Sollima stages it, are some of the picture’s greatest weaknesses.

Not that the screenplay is otherwise always clear or coherent; Graver’s plan is certainly complex, but there are points when it seems not only needlessly so but incompletely thought-through. The flaws are mitigated, though, by Sheridan’s ability to insert tart lines of dialogue and the many invitations he provides for Sollima to flex his muscles in choreographing large-scale action sequences where the vehicles do all sorts of stunts and the blood flows freely.

Del Toro, meanwhile, expands on the character he created in 2015, giving Alejandro a range of emotion that he hadn’t previously possessed. It’s really his movie, though newcomer Moner complements him nicely in their long trek together—punctuated by an appealing quiet interlude with a deaf farmer (Bruno Bichir) and his family. Brolin is fine as well, but Graver doesn’t offer him much in the way of nuance, and he comes across as slightly stolid. Fortunately Jeffrey Donovan is on hand as his lieutenant, bringing a dose of wry humor to the proceedings. Modine and Keener are suitably bland as establishment types lacking in cojones, while Rodriguez is good, if not outstanding, as a young man going through a wrenching transformation.

Like “Sicario,” “Soldado” is technically outstanding. Stepping in for Roger Deakins, cinematographer Dariusz Wolksi brings a palpable sense of desolation and menace to the arid desert locations, while the deep moaning sounds fashioned by composer Hildur Gudnadottir are as successful in maintaining a mood of foreboding as Johann Johannson’s strange sounds were in the earlier picture. And though it runs a full two hours, “Soldado” doesn’t drag, thanks to Matthew Newman’s skillful editing.

Though not as fully satisfying as Villeneuve’s film, Sollima’s is a worthy successor to it, and perhaps a stepping-stone to future installments in a larger saga set along the southern border.