Russian agents have been accused of using online propaganda and computer hacking to undermine democratic processes in the United States and several European countries.
The Kremlin dismisses such allegations, but a probe into whether US President Donald Trump's 2016 campaign colluded with Russia has triggered a bitter political crisis in the US.
Reports this week suggested Washington fears that Mexico will also see such interference in July, when voters will choose a successor to President Enrique Pena Nieto.
"We hear this from our European counterparts as well. My advice, to Mexico, would be pay attention. Pay attention to what's happening," he said.
At a speech Wednesday to mark the start of a five-nation tour, Tillerson warned that Russia and China are seeking to expand their influence in Latin America and urged the region to stand by the values of the "democratic hemisphere.