Tillerson, in a speech ahead of a visit to Mexico, Argentina, Peru, Colombia and Jamaica, said China was getting a foothold in Latin America, using economic statecraft to pull the region into its orbit.
The government there has faced widespread criticism over its decision to push up presidential elections under conditions that opponents say overwhelmingly favor President Nicolas 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.
At a weekend news conference in Buenos Aires, a senior state department official said the comments were not helpful, reported Reuters.
"Because not doing anything to bring this to an end is also asking the Venezuelan people to suffer for a much longer time", he said.
The day before in Austin, Texas, Tillerson said it is a tragedy that Venezuela could be one of the most prosperous countries in the region but instead is of the poorest in the world - "all the result of man-made collapse". We want it to be a peaceful change.
The economic crisis has forced thousands to cross the border to neighbouring countries.
Indian firing across LoC martyrs one, injures two: ISPR
On Sunday, four Indian soldiers were killed and four other persons were injured in the firing in Rajouri and Poonch districts. Meanwhile the district administration Rajouri has closed all 84 schools located near the LoC for three days.
The Secretary of State, who has been travelling through several Latin American countries since February 1, will meet with President Juan Manuel Santos and he is due to discuss bilateral relations between the two countries, which have traditionally had good connections.
"Our disagreements are with the Venezuelan regime, not the Venezuelan people", Tillerson said.
"Rex Tillerson visiting Argentina just threatened us with a oil embargo", Maduro said on Facebook. "We have advocated that they return to the constitution", he stated, adding that Maduro's political fate will depend on the outcome of elections.
In a prelude to the tour, the secretary of state made thinly veiled reference to USA support of a military coup in Venezuela to overturn the Maduro government at the University of Texas at Austin, last Thursday. In other words, the time may be ripe to play the oil import card without affecting US refiners too severely.
Analysts say USA oil sanctions could completely cripple the Venezuelan economy.
"I assume the administration will not pursue this policy if it means gas prices go up, especially when the midterm elections are dicey already", Weeks added.