Tillerson specifically said Maduro needs to dissolve the Constituent Assembly, which was created a year ago and quickly sacked the country's attorney general, who was a critic of Maduro.
Local experts referred the possibility that those agreements will translate into actions against the Venezuelan government, in tune with Tillerson's calls during his tour to take that kind of measures, while considering the possibility of "oil sanctions" against Caracas.
Tillerson's visit has raised comments by social organization that have noted that the USA secretary of state's tour aims to "tighten up on the presidents who are Washington's agents", as they describe Enrique Peña Nieto (Mexico), Mauricio Macri (Argentina), Juan Manuel Santos (Colombia) and Pedro Pablo Kuczynski (Peru).
"In the history of Venezuela and South American countries, it is often times that the military is the agent of change when things are so bad and the leadership can no longer serve the people", Tillerson said at the University of Texas in Austin on Thursday.
Venezuela has announced the issuance of an oil-backed cryptocurrency, petro.
The current visit of U.S. Secretary of State Rex Tillerson seeks stronger bilateral, trade ties with Peru, foreign affairs analyst Juan Velit affirmed.
Last year's Pew Research Center poll also revealed that 65 percent of Mexicans express a negative opinion of the U.S. as compared to 29 percent in 2015.
Argentine Foreign Minister Jorge Faurie responded that his country would "closely follow" possible oil restrictions but added that sanctions "must never harm the Venezuelan people".
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Donald Trump y Nicolas Maduro. "We are prepared, Venezuela, workers of the oil industry, imperialism threatens us, we are ready to be free and no one is going to stop us", he declared.
"This is under study, it's under consideration", Tillerson said about the potential sanctions.
"[While] over there visiting Argentina, Rex Tillerson just threatened us with an oil embargo".
Experts and analysts have also warned that such sanctions could have negative effects on the U.S. oil industry and consumers.
The socialist incumbent was officially named his party's candidate on Friday, the same day that Tillerson kick-started his week-long Latin American and Caribbean tour that began in Mexico.
Cuba's Foreign Ministry said that it saw the secretary of state's remarks as an effort to "instigate openly an overthrow, by any means", of the Venezuelan government, likely alluding to Tillerson's remarks last week about the potential for the Venezuelan military to oust Maduro - a comment that came months after Trump said the U.S. could take military action.