As Maduro told supporters in Caracas to prepare for an "imperialist" invasion, U.S. Vice President Mike Pence sought to calm concerns in the region about Trump's talk, promising a peaceful solution to Venezuela's "collapse into dictatorship".
Pence said he expects a "breakthrough" soon on commodity agreements with Argentina that may include products such as US pork, Argentine beef and lemons.
"If they don't show up on their own, we'll go looking for them with handcuffs", he told a few thousand government supporters, many of them state workers, gathered at the presidential palace.
The rest of Latin America - even countries that condemn President Nicolas Maduro's attacks on Venezuela's democratic institutions - have strongly rejected the threat.
Mark Scheider, an adviser at the Americas program at the Center for Strategic and International Studies, says Trump's remark was a setback for the fragile regional alliance against Maduro's increasingly authoritarian government.
'President Trump is a leader who says what he means and means what he says, ' Pence said.
Pence later boarded his plane to fly to Argentina, the second stop on a tour that will also take him to Chile and Panama. "The U.S. has many options for Venezuela".
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The attacks are a risky approach considering Trump's slumping job approval ratings among his most fervent supporters. But they continue to butt heads with a White House that's unhappy with where they left the health care debate.
Pence listened to the stories of people who had fled from the country Monday. And you can be assured, Mr. President, we will continue to take action until the Maduro regime restores democracy, holds free and fair elections, releases all political prisoners, and ends the repression of the Venezuelan people. President Santos simply responded that "military intervention would be unacceptable to all countries in Latin America".
U.S. Vice President Mike Pence spoke on the violence in Charlottesville, Virginia, during a news conference in Colombia on Sunday (August 12). "Let us preserve it as such". Trump's comments on Friday have fuelled long-standing accusations that the U.S. is preparing a military attack. And the media hasn't been focused on "what the president said", it's been criticizing what the president didn't say.
Central Intelligence Agency director Mike Pompeo said Mr Trump, by raising the prospect of possible military action, was trying "to give the Venezuelan people hope and opportunity to create a situation where democracy can be restored".
Venezuela's economy is heavily reliant on its oil exports.
The United States accuses him of a power grab that has sparked deadly protests and condemnation across the region.