PANAMA CITY, Panama — Secretary of State Mike Pompeo said Thursday that he had warned President Juan Carlos Varela of Panama about doing business with China, criticizing Chinese state-owned enterprises that engage in “predatory economic activity.”

As his plane left Panama City, Mr. Pompeo recounted his talks with Mr. Varela and local journalists. Clearly concerned that Panama could become a beachhead for growing Chinese economic influence in the Western Hemisphere, he emphasized that Panamanians should be cautious when considering business ties with China.

Mr. Pompeo said he intended to tell the entire region that “when China comes calling, it’s not always to the good of your citizens,” and that countries had to watch out for Chinese companies that “show up with deals that seem too good to be true.”

His warning came more than a year after Panama cut diplomatic relations with Taiwan — which China views as a part of its territory — in favor of establishing ties with Beijing. Two other nations in the region followed suit this year.