Tillerson's Mexico City visit is the first leg in a week-long Latin America trip in which he hopes to keep up pressure on Venezuelan President Nicolas Maduro over his restrictions on domestic political opposition.
Diplomats have said that such harsh rhetoric from the president impedes the broader mission of Tillerson and other State Department envoys who seek to build relationships to further the US agenda.
The United States and Mexico have had tense relations over President Donald Trump's proposals to curb illegal immigration and have Mexico pay for a reinforced border wall.
The State Department has said the trip is centered on the "crisis in Venezuela", where the United States has imposed financial sanctions in an attempt to spur democratic change. He suggested that, unlike China, "we do not seek short-term deals with lopsided returns" in the region.
"All I can say to you is that we know that Russian Federation has fingerprints in a number of countries around the world", Tillerson said during a news conference with Mexican Foreign Minister Luis Videgaray.
"China is a major worldwide buyer of Latin American bulk commodities, and imports more and more agricultural and high value-added products from the region", the ministry said. "We can lift more people out of poverty". "You can not expect to have one without the other".
Tillerson later held a closed-door meeting with Mexican President Enrique Pena Nieto during a time when relations have also been strained by USA threats to pull out of the North American Free Trade Agreement (NAFTA).
Mexico and Canada's top diplomats also played down tensions, despite Trump's tirades and a recent series of trade disputes between the Washington and Ottawa.
Freeland said Trump and Canadian Prime Minister Justin Trudeau "really get along" and called Tillerson "an incredibly important voice in maintaining the rules-based worldwide order".
"The U.S. would need to step away from meddling so much in the governments, in their elections, in their development", Zavala said.
He has repeatedly accused the United States of leading an worldwide plot to oust him and undermine the social programmes introduced by the socialist party since it came to power in 1999. Former Argentinian Ambassador to Venezuela Alicia Castro told news outlet Sputnik that the trip "aims to coordinate undermining of Maduro's government", and added that the US sole objective is to "capture Venezuelan oil".
"What we would like to see happen there is a peaceful transition", Tillerson said, denying accusations from Caracas of plotting a violent ouster.
Along with Washington it has rejected as undemocratic the Venezuelan government's decision to hold "snap" presidential elections.