"Venezuela is sliding into dictatorship, and as President Trump has said, the United States will not stand by as Venezuela crumbles," Pence said.
Noting that the United States reserves "many options for Venezuela," Pence added, "President Trump is a leader who says what he means and means what he says, but the president sent me here to continue to marshal the unprecedented support of countries across Latin America to achieve by peaceable means the restoration of democracy in Latin America, and we believe it is achievable by those means."
Pence's comments came at a joint news conference with Colombian President Juan Manuel Santos on Sunday evening at the oceanfront presidential compound in Cartagena, where Santos later hosted Pence and his wife, Karen, for a casual dinner.
Colombia is one of the United States' closest allies in the Western Hemisphere, yet, as he stood next to Pence, Santos denounced Trump's threat of military action, and told the visiting vice president that such a possibility "shouldn't even be considered" and would be "unacceptable."
"Every country in Latin America would not favor any form of military intervention, and that is why we are saying we are intent on looking into other measures, some of which are already underway and others to be implemented in the future," Santos said.
Pence's six-day visit to Colombia, Argentina, Chile and Panama is expected to be dominated by the turmoil in Venezuela, although he also is planning to highlight trade and security partnerships throughout the hemisphere.
Maduro's autocratic government seized power last month and has cracked down on dissent, precipitating an economic collapse and drawing international condemnation.
Pence said he and Santos discussed during a private meeting additional economic sanctions and other measures to increase pressure on Venezuela.
Trump's bellicose threat, delivered Friday from his private golf course in New Jersey, generated banner news headlines across Latin America because it harked back to a generation of American imperialism.
"It is one thing for the U.S. president or vice president to discuss sanctioning the regime and our support for the return of democracy," said Richard Haass, president of the Council on Foreign Relations. "It is something else to discuss U.S. intervention, which only strengthens Maduro's hand and makes it harder for other regional countries to work with us."
Pence arrived in South America to add his voice to the coalition of nations trying to isolate Venezuela and pressure Maduro to change course. In a watershed development, 11 Latin American countries and Canada signed a hard-hitting resolution last week that calls the Venezuelan government illegitimate and demands a return to democracy.
"Vice President Pence now needs to assure regional allies that the United States respects their diplomatic efforts and will not engage in unilateral measures that are guaranteed to be counterproductive," said David Smilde, a senior fellow at the Washington Office on Latin America and a Venezuela expert at Tulane University.
Pence plans to spend less than 24 hours in Colombia. He will fly midday Monday to Buenos Aires, where he will meet Tuesday with Argentina's president, Mauricio Macri, and give a speech about regional trade and security partnerships to representatives of the Argentine and Latin American business community.
Pence then will visit Santiago, Chile, on Wednesday, where he will meet with President Michelle Bachelet and deliver remarks that evening to representatives of the Latin and Central American business community.
On Thursday and Friday, Pence will visit Panama City, where he will meet with President Juan Carlos Varela and tour the newly expanded Panama Canal.
This is Pence's first visit to South America, although he has previously talked with the four leaders, either in person, such as at the White House, or by phone. Karen Pence plans to meet with art therapists and observe art therapy sessions in some of the countries, as well as participate in cultural activities.
A senior administration official said the four countries the vice president will visit are "key partners and friends of the United States" — in marked contrast to Venezuela. Although the Venezuelan crisis is top of mind, Pence plans to highlight other issues as well.
For instance, Pence pressured Santos to curb the flow of drugs into the United States, including reducing the surging levels of coca production in Colombia, which he called "our greatest concern" about the country.
"This worsening crisis requires swift action to protect the people of both our countries," Pence said, standing next to Santos. "The drug trade is a wellspring of violence, crime and corruption victimizing the Colombian people. In the United States, illegal drugs coming from Colombia have poisoned our children, torn apart our families and devastated too many communities. Mr. President, this must end, and this must end soon."