In fact, the small section of wall that Mr. Trump stood in front of — next to a field of solar panels — is not evidence that the president is building the wall he repeatedly called for during his 2016 presidential campaign but merely an upgrade to an existing section of fencing. The two-mile section was completed in October.

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Weeks after declaring a national emergency at the border because Congress refused to fund construction of his border wall, Mr. Trump recently threatened to close the legal ports of entry between Mexico and the United States — potentially disrupting billions of dollars’ worth of trade and halting the travel of a half-million people each day.

But on the eve of his trip here, Mr. Trump backed down in the face of hard criticism from the business community and top officials in his own party. Senator Mitch McConnell, the Republican leader, predicted that a complete border shutdown would have a “potentially catastrophic economic impact” on the country.

Mr. Trump responded on Thursday by initially saying he would give Mexico a year to stop Central American migrants from traversing Mexico on their way to the United States. He added that if Mexico did not do its part, he would first impose tariffs on Mexican cars before shutting down the border.

Later in the day, Mr. Trump denied that he had put off a border shutdown for a year, saying that it could still happen if he decided that Mexico was not doing enough to keep migrants from traveling to the United States.

“We’ll start with the tariffs and see what happens,” he said.

In his visit here, Mr. Trump thanked Mexico for deporting migrants at its southern border, which he said “they have never done before” in three decades, and suggested he had delayed closing the border because of their heightened efforts.