On Mr. Christie’s itinerary: a session at the National Palace with President Enrique Peña Nieto, with whom the governor hit it off last year at the annual Allen & Company investment conference in Sun Valley, Idaho; conversations with senior political officials; and a round-table discussion with New Jersey and Mexican business executives.

After struggling in 2009 to appeal to Latinos, who make up 19 percent of New Jersey’s population, Mr. Christie has become their candidate of choice in New Jersey. He earned plaudits from Hispanic groups when he signed legislation last year granting lower state college tuition rates to students without legal immigration status who have attended three years of high school in New Jersey, and he has struck a conspicuously measured, compassionate tone when discussing the Central American children now crossing the border.

“We are an empathetic people in this country and we don’t like seeing people suffer,” he said recently when asked about them. At the same time, Mr. Christie has carefully avoided taking specific positions on the divisive legislative fights in Washington over how to address the problem.

There are no plans for Mr. Christie to visit the United States’ southern border with Mexico, where Central American children are now pouring into Texas. But the controversy, and both countries’ options for resolving it, will inevitably be broached in Mr. Christie’s meetings with Mexican leaders, those planning the trip said.

“A visit like this,” said Mr. Sobel, “will broaden the governor’s learning on a lot of these issues when he’s there.”

Mr. Paul, who has stood out within the likely 2016 Republican field for his aggressive, unconventional courtship of minority voters, will arrive in Guatemala in mid-August with a team of Utah medical experts who will treat poor rural residents with eye problems, most of them cataracts.

Image Senator Rand Paul of Kentucky will travel to Guatemala, where he will put his ophthalmology training to use by treating local patients with eye disorders. Credit... Charlie Neibergall/Associated Press

Michael Yei, who is coordinating the trip from the University of Utah, said it was Mr. Paul who proposed the Central American location. “He ended up saying, ‘How about Guatemala?’ ” Mr. Yei recalled.