He also pitched the United States as the region's strongest partner at a time when countries like Russian Federation and China continue to make inroads into Latin America. He later added that "China's state-led model of development is reminiscent of the past".
CGTN's Franc Contreras reports from Mexico City.
The U.S. will continue trying to pressure Venezuelan President Nicolás Maduro to return his country to the democracy established by its constitution but will not press him to step aside, Tillerson said.
Mexico holds presidential and congressional elections on July 1 and so far the frontrunner in nearly all polls is left-wing former Mexico City Mayor Andres Manuel Lopez Obrador.
Speaking in Austin, Texas just before departing, Tillerson said economic prosperity in Latin America goes hand-in-hand with regional security.
Acknowledging that US demand for drugs is driving the cartels' violence and lawlessness, Tillerson said the U.S.is working with other countries to find strategies to attack the organizations' revenue streams, halt the transfer of weapons from the USA and find and prosecute "the middlemen who enable them".
Tillerson flew out Friday evening for Argentina, and will then visit Peru, Colombia and Jamaica, pushing for stronger action on Venezuela and touting his vision of deeper cooperation.
Tillerson is also expected to rally the region's governments in pressing democratic reforms in crisis-ridden Venezuela.
"And importantly, we share democratic values, values that are the core of what we believe, regardless of the color of our passport".
With the Colombian civil war officially over, a number of USA lawmakers have apparently claimed that former FARC guerrillas have now joined the ranks of the country's sizeable army of drug manufacturers and traffickers. "Ineffective and corrupt governments damage countries, the economy suffers, people lose faith in institutions and crime increases".
Also, the Los Angeles Times reports that several Latin American countries, including Mexico, had earlier voiced their concerns about Trump's intent to renegotiate the North American Free Trade Agreement (NAFTA), warning that they may reconsider their cooperation with the United States on other matters if the deal breaks down. Trump insists on building what he calls "a great border wall" that would further separate Mexico from the U.S. In his State of the Union address earlier this week, Trump emphasized his plans for a continued U.S. crackdown on immigrants.
He called on Latin America to do the same. She said it's time for all sides to see that the USA and Latin American nations are permanent neighbors.
"In terms of timelines, we would love to get this deal done as quickly as possible", Canadian Foreign Affairs Minister Chrystia Freeland said in a news conference. "If we can set those limits very clearly, I think will be good enough".