Even Mr. Christie could not resist drawing attention to the parallels. “If and when I become a candidate for president of the United States,” he said in response to one question here. “Until I become a candidate for president of the United States,” he replied to another.

A campaignlike air pervaded his events, whose locations seemed to be chosen for their cinematic backdrops. In Mexico City, he spoke inside the courtyard of the historic Secretariat of Education building, surrounded by large, colorful murals by the artist Diego Rivera. In Puebla, Mr. Christie took the podium at the top of a city park of restored forts with sweeping views of the city.

On Friday afternoon, Mr. Christie walked into a high school stadium here filled with 2,000 cheering children, many of them waving the New Jersey flag — a crowd that would rival anything he might draw in Iowa. As the governor sat on a dais high above, with his name emblazoned on a billboard, a few dozen high school students dressed in traditional Mexican garb acted out scenes from the country’s history and a marching band struck up American pop tunes (a highlight: Bruno Mars’s “Treasure”).

Afterward, Mr. Christie declared himself “overwhelmed.”

There was a TV-ready quality to his schedule. Aides rushed reporters and photographers into many of his meetings for a few moments, to briefly witness Mr. Christie at work, then commanded them to leave. Inside the school stadium, his staff repeatedly repositioned reporters for the best possible shot of Mr. Christie, who seemed to bask in the presidential-style trappings and treatment.