But first he will have to overcome the aftermath of Trump's aggressive brand of diplomacy.
The US-Mexican relationship has been strained by Trump's attacks on Mexican immigrants and the North American Free Trade Agreement - and his insistence on building a border wall.
The trip will be an effort to reassure nations that the US remains interested in a region that under President Donald Trump is mentioned mostly as a source of illegal immigrants and crime.
The top USA diplomat is expected to use his time in the region to build a coalition that would levy political and economic sanctions against the governments of Nicolas Maduro in Venezuela, and Raul Castro in Cuba.
To lay the groundwork, he appeared at his alma mater, the University of Texas, to flesh out the Donald Trump administration's approach to its southern neighbors.
After the speech, the 65-year-old former oil executive was to fly to Mexico for a working dinner with Foreign Minister Luis Videgaray and senior United States and Mexican legal and security officials.
There can be no economic development in the hemisphere without security, and no security without stronger economies, Tillerson said in a half-hour speech at the University of Texas.
It is becoming increasingly likely NAFTA talks will extend through 2018.
After visiting Buenos Aires and the Argentine mountain resort town of Bariloche, Tillerson is scheduled to head to Lima to meet with Peruvian President Pedro Pablo Kuczynski on issues including the eighth annual Summit of the Americas, set for April 13-14 in Lima.
Tillerson, who is on his first multi-nation mission to Latin America, delivered the policy address in his home state, at his alma mater, the University of Texas in Austin, an institution steeped in studies of US relations with Central and South America.
US Secretary of State Rex Tillerson has warned that China and Russian Federation are assuming "alarming" roles in Latin America and urged regional powers to work with the United States instead.
"Latin America does not need new imperial powers that seek only to benefit their own people", Mr Tillerson said.
He also went on the offensive against the leftist government of Venezuela, once a rival center of influence for Latin American nations, now a political and economic basket case.
Tillerson said on Thursday that the Venezuelan military could decide to oust President Nicolas Maduro, but said he did not know whether that would happen.
The United States has imposed several rounds of sanctions on 50 senior officials from the Maduro government including President Maduro and Vice President Tareck El Aissami.
Luz Maria de la Mora is an expert on US and Latin American diplomacy.