MEXICO CITY — Secretary of State Rex W. Tillerson on Friday took on the daunting task of resetting relations with Latin America, a region where President Trump’s anti-immigrant invective and his disdain for trade ties are rattling allies of the United States.

Nowhere have the insults been felt more keenly than in Mexico, where Mr. Tillerson began a tour of the region by assuring his hosts that he was committed to preserving the North American Free Trade Agreement signed by Mexico, the United States and Canada.

“I cannot emphasize enough the importance of our economic relationships,” Mr. Tillerson said after meeting with the Mexican and Canadian foreign ministers, acknowledging that almost three million American jobs depend on trade with neighboring countries.

Like much of what Mr. Tillerson said on Friday, the statement seemed to contradict his boss. Mr. Trump has called Nafta “the worst trade deal ever made” and has repeatedly threatened to pull the United States out of the accord, which took effect in 1994.