MEXICO CITY — In 1982, when gunmen attacked a police station in rural Peru, President Fernando Belaúnde Terry blamed guerrillas from the Shining Path and called the crime an act of “narco-terrorism — the union of the vice of narcotics with the violence of terrorism.” With that, he coined a term that fused two major nemeses of the United States — drugs and terrorism — into a single battle cry.

President Trump revived this idea in an interview last week with the former Fox News host Bill O’Reilly. “Are you going to designate those cartels in Mexico as terror groups and start hitting them with drones and things like that?” Mr. O’Reilly asked. “I don’t want to say what I’m going to do, but they will be designated,” Mr. Trump responded. “I have been working on that for the last 90 days.” He was referring to putting some of the cartels on the State Department’s list of foreign terrorist organizations.

Predictably, Mr. Trump’s comments were received with enthusiasm by hard-liners such as Representative Mark Green, who has called for the action in the past. “These cartels use barbaric ISIS and Al Qaeda tactics to murder and torture innocents, destabilize countries, and assassinate members of law enforcement,” he said in a tweet. And it sparked some protest south of the Rio Grande with the Mexican foreign minister, Marcelo Ebrard, declaring Mexico would not tolerate any “violation of its sovereignty” — meaning United States military strikes against cartels here.

The action fits comfortably into the president’s wider narrative of defending the southern border against dangerous foreign threats. But it could also lead to a series of far-reaching consequences, some of them dangerous.