In his most important regional policy statement since his appointment, Tillerson also warned Latin American countries against excessive reliance on economic ties with China, while sounding alarm over Russia's growing presence.
"While this trade has brought benefits, the unfair trading practices used by many Chinese have also harmed those countries' manufacturing sectors, generating unemployment and lowering wages for workers", the U.S. Secretary of State said.
After visiting Buenos Aires and the Argentine mountain resort town of Bariloche, Tillerson is scheduled to meet in Lima with Peruvian President Pedro Pablo Kuczynski on various issues, including the eighth annual Summit of the Americas, which is to be held April 13-14 in Lima, Peru.
After the speech, the 65-year-old former oil executive was to fly to Mexico for a working dinner with Foreign Minister Luis Videgaray and senior U.S. and Mexican legal and security officials. "We have advocated that they return to the constitution", Tillerson said.
Several students in attendance were given the opportunity to ask Tillerson questions.
President Donald Trump's top diplomat returned to his alma mater, where he had performed with the Longhorn Band, on the eve of a seven-day trip to Mexico, Argentina, Peru and Colombia.
Mexico has been at pains to prove itself a good ally to the United States on combating drug trafficking and immigration, in hopes this would help efforts to renegotiate the North American Free Trade Agreement on as favorable terms as possible.
To lay the groundwork for his trip, he first gave a wide-ranging speech on the Trump administration's approach to the region.
As the US Secretary of State embarks upon his voyage across the region that the United States has long considered its own backyard since the implementation of the Monroe Doctrine in 1823, it's unclear exactly how receptive the countries he's about to visit will be to his message.
His attitude to the countries south of the Rio Grande might best be symbolized by his multi-billion-dollar efforts to build a wall across the United States border with Mexico, to keep out illegal immigrants and drugs. According to a recent survey by Gallup, only 16 percent of Latin Americans approve of Trump's job and they expect relations to worsen rather than to improve.
Tillerson also spoke about the region more broadly, emphasizing that collaboration among countries Western hemisphere would bolster all their economies.
At the end of Tillerson's visit, William Inboden, executive director of the Clements Center, asked for the secretary's thoughts on what he called Texas' "most threatening border problem" - Oklahoma.