As he has moved the United States toward a more protectionist stance on trade, Mr. Trump has abandoned the Trans-Pacific Partnership, which includes Mexico, Peru and Chile. The United States is also engaged in difficult negotiations with Mexico and Canada over changes to the North American Free Trade Agreement.

In Colombia, Mr. Trump will be repaying a visit Mr. Santos, a Harvard-trained economist who won the Nobel Peace Prize in 2016 for negotiating a peace treaty with FARC guerrillas, made to the White House in May. At a news conference with Mr. Trump at the time, Mr. Santos sidestepped a question about whether he agreed with the White House’s plan to build a wall on the border with Mexico to halt the flow of drugs into the United States.

Earlier, Mr. Trump had said that coca cultivation and cocaine production had risen to record levels in Colombia, and challenged Mr. Santos to remedy the problem. The United States has a long history of cooperation with Colombia on that issue and others.

The efforts to build the border wall, along with the president’s move in recent days to establish tariffs on steel and aluminum imports, have inflamed some of the leaders with whom he will meet in Peru. After vocal protests from Mexico and Canada, Mr. Trump granted those countries a temporary exemption from the tariffs. But Brazil, a major steel exporter to the United States, has not been given any such exemption.

American presidents have attended the Western Hemisphere meeting, known as the Summit of the Americas, in previous years — Barack Obama made history there in 2015 by meeting with President Raúl Castro of Cuba — but few have stoked as much indignation as Mr. Trump.