Dave Clark - The United States' top diplomat set out a vision for a free and prosperous Americas on Thursday, damning what he called the failed model of Venezuela's "corrupt and hostile" regime.

Secretary of State Rex Tillerson gave a wide-ranging speech to better define US strategy in its home "democratic hemisphere," before setting off on a major tour of Latin American countries.

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.

In his first year in office, President Trump has decried free trade with Mexico, US detente with Cuba, and warned of the dangers of drug gangs and illegal immigration.

His attitude to the countries south of the Rio Grande might best be symbolized by his multi-billion-dollar efforts to build a wall across the US southern border with Mexico, to keep out illegal immigrants.

But Tillerson, who is often left with the task of explaining why Trump's "America First" slogan does not mean "America Alone," was keen to tout a more positive approach to relations.

"We share an interwoven history and chronology. Our nations still reflect the New World optimism of limitless discovery," he told staff and students.

"And importantly, we share democratic values, values that are the core of what we believe, regardless of the color of our passport."

Speaking hours before he was due in Mexico City to discuss security and immigration with top officials, he warned of the need to fight violent drug cartels.

Trump made great play of this in his annual State of the Union address on Tuesday, when he cited crimes of the Salvadoran MS-13 gang to justify his hardline stance on immigration.

"The most immediate threat to our hemisphere are transnational criminal organizations, or TCOs," Tillerson said. "In their pursuit of money and power, TCOs leave death and destruction in their wake."

Washington's other bugbear is Venezuela's beleaguered leftist regime, which in earlier years was a rival center of influence for Latin American nations seeking a way out of poverty.

The United States has had a troubled relationship with much of Latin America where, during the Cold War, it placed Cuba under embargo and often supported dictatorial right-wing regimes against social reformers.

Charismatic late president Hugo Chavez's oil-fuelled support for socialist-leaning allies, and domestic social welfare projects, were an attractive alternative for many.

But under current leader Nicolas Maduro, and with world oil prices down, Venezuela faces economic collapse and widespread popular protest - even as US allies like Colombia emerge from decades of conflict.

Warns of 'imperial powers'

Tillerson turned the screw, laying out a different path to prosperity.

"The corrupt and hostile regime of Nicolas Maduro in Venezuela clings to a false dream, an antiquated vision for the region that has already failed its citizens," he said.

Tillerson noted that the United States, Canada and European Union have imposed economic sanctions targeting Maduro loyalists seen as profiteers or human rights abusers.

He called on Latin America to do the same. The continent's major powers reject the regime, but are cautious about piling on more economic misery with Venezuela on the brink of chaos.

How the countries of South and Central America see their own future will be very important this year, with potentially defining polls in Brazil, Argentina and Mexico.

Tillerson warned that China and Russia are assuming "alarming" roles in Latin America and urged regional powers to work with the US instead.

"Latin America doesn't need new imperial powers that seek only to benefit their own people," he said.

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 US and Mexican legal and security officials.

On Friday he is to meet President Enrique Pena Nieto before heading on to his next engagement at the Andean resort of Bariloche, Argentina, and then to Buenos Aires on Monday.

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.