TIJUANA, Mexico — With the bullhorn of a nationally televised address and the prestige of the White House around him, President Trump delivered a dark, if familiar, message to the American people on Tuesday night: The United States needs a border wall to stanch the flow of drugs and criminals, and it has no more room for migrants.

In Mexico — the supposed origin and pipeline of these menaces — leaders and citizens reacted with a weary shrug.

In the Mexican border city of Tijuana, where thousands of migrants have gathered seeking entry to the United States, most of the televisions in a downtown restaurant showed soccer matches and basketball games. Mr. Trump’s voice, nearly drowned out by music, emerged faintly from a screen in the back.

Almost no one seemed to care, or even listen to what the American president had to say.

Luis Arce, a 32-year-old lawyer, was among the few who took a moment to reflect on Mr. Trump’s speech. He said he was not surprised by Mr. Trump’s insistence on building a wall, nor by anything else in the remarks.