"China, as it does in emerging markets throughout the world, offers the appearance of an attractive path to development, but in reality this often involves trading short-term gains for long-term dependency", Tillerson said.
"The great tragedy of Venezuela is that, although it could be one of the most prosperous countries in the region, it is one of the poorest, " Tillerson said. "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.
"Venezuela and Cuba reminded us that... we must prioritize and promote democratic values", according to Tillerson. "My advice would be... pay attention to what's happening".
Many Latin Americans read that as a focus on people coming from their region.
On some positions, Trump has softened his rhetoric since his inauguration a year ago, but in this week's State of the Union address he spoke more about cross-border crime and immigration than any other foreign policy topic. "In their pursuit of money and power, TCOs leave death and destruction in their wake".
"The development of China-Latin America ties does not target or reject any third party, nor does it affect the interests of third parties in Latin America", he said, expressing hope that relevant countries abandon the outdated concept of zero-sum game and look at the development of China-Latin America relations in an open and inclusive manner.More news: Brendan Cole has danced his last Strictly
The three officials said they also discussed the political and economic crisis in Venezuela and its government's decision to push up presidential elections to April under conditions that opponents say overwhelmingly favor President Nicolas Maduro, who is so far the only candidate.
But under current leader Nicolas Maduro, and with world oil prices down, Venezuela faces economic collapse and widespread popular protest - even as U.S. allies like Colombia emerge from decades of conflict.
Accusing Washington of seeking to undermine democracy in Latin America and return to the days of "imperialism", Defense Minister Vladimir Padrino lashed out at Mr Tillerson during a broadcast on state television.
Ahead of a diplomatic trip across the Western Hemisphere, Secretary of State Rex Tillerson outlined a foreign policy of economic growth, security and democratic governance to engage with the region he deemed a "priority" for the country. Tillerson is also due to meet with President Enrique Pena Nieto.
Before arriving back in Washington late on Wednesday, he is to visit Peru - host of an upcoming Summit of the Americas - as well as Colombia and Jamaica.