PANMUNJOM, South Korea — Defense Secretary Jim Mattis’s visit to the Korean Peninsula’s extremely militarized demilitarized zone on Friday was meant to show American solidarity with South Korea against a muscular North, which Mr. Mattis accused of building nuclear weapons to “threaten others with catastrophe.”

But the trip also highlighted the central contradiction in the Trump administration’s rhetoric on North Korea: that for all the talk of military options, there really aren’t any — at least, none that wouldn’t put the sprawling city of Seoul, with its population of 10 million, in the cross hairs of thousands of Pyongyang’s artillery installations.

Standing side by side with Mr. Mattis atop an observation post to gaze at the North, South Korea’s defense minister, Song Young-moo, seemed at times to be giving his American counterpart a guided tour of how a strike against North Korea’s nuclear facilities would quickly trigger retaliation.

“There are 21 battalions” stationed over the border, Mr. Song told Mr. Mattis, gesturing toward the hills of North Korea in the distance. “Defending against this many L.R.A.s is unfeasible, in my opinion,” he said, alluding to the bristling array of long-range artillery pointed at his country.