Tillerson also talked about the USA helping law enforcement in Mexico - providing inspection equipment and training - to help put an end to smuggling of drugs and people. The Mexican Coordinator of Solidarity with Venezuela rejected the presence here of the representative of the Donald Trump administration, and declared him persona non-grata.
Tillerson also criticized Russian Federation for selling weapons to authoritarian governments in Latin America.
Countering the barrage of tirades coming from their northern neighbor, Mexican voters, according to polls, have rallied behind Andres Manuel Lopez Obrador, a leftist nationalist and former mayor of Mexico City, as their preferred presidential candidate. In Austin, Texas, Tillerson said "China's state-led model of development is reminiscent of the past".
On Friday he is to meet President Enrique Pena Nieto before heading on to his next engagement at the Andean resort of Bariloche, Argentina, and then to Buenos Aires on Monday.
After Mexico, Tillerson - who is often left with the task of explaining why Trump's "America First" slogan does not mean "America Alone" - is set to travel on to Argentina, Peru, Colombia and Jamaica, touting his vision of deeper cooperation. They're expected to discuss not only Venezuela but also "the surge in coca cultivation and cocaine production, economic issues and the growing refugee population" from neighboring Venezuela, the State Department said.
Venezuela is in its fifth year of a worsening political and economic crisis.
"We do not seek short term deals with lop-sided returns", Tillerson said.
"When individuals are living in poverty, a life of crime can look like the only opportunity available to make a living, legal and illegal immigration increases as people look for more opportunity elsewhere, and innocent people are more likely to become victims of drug cartels, human traffickers and corrupt law enforcement", he said.
Two other contentious issues between the two countries - President Trump's promises to build a new border wall and to deport large numbers of unauthorized immigrants - are looming, but the renegotiation of the North American Free Trade Agreement could have the most imminent impact. "The trip reflects President [Donald] Trump's realization that we need to stop drug inflows, work harder with allies and take a page from history", he said.
He called on Latin America to do the same.
"Obviously that would be something that we strongly want to avoid", Videgaray said at an event in NY late a year ago, reffering to NAFTA collapsing.
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