The US vowed Monday to stop Venezuela from becoming a "failed state," as it rallied Latin American allies after Trump warned of possible military action.
US Vice President Mike Pence met in a church in Cartagena, Colombia with Venezuelan families who have fled their country's deadly crisis, as he wrapped up the first stop on a Latin American tour.
"We will not stand by as Venezuela crumbles, but it's important to note, as the president said, that a failed state in Venezuela threatens the security and prosperity of the hemisphere," Pence told reporters.
He told CNN in an interview that Venezuela risked becoming "a greater problem for narcotics traffic" and "greater migration" -- both of which he said directly threatened the security and economy of the US.
Pence later boarded his plane to fly to Argentina, the second stop on a tour that will also take him to Chile and Panama.
On Sunday, Pence stood by Trump's threat, saying the US president "says what he means and means what he says."
But he expressed hope a "peaceable solution" could be found on Venezuela.
Trump on Friday said he was mulling a range of scenarios for crisis-hit Venezuela -- "including a possible military option if necessary."
Caracas condemned the comment. On Monday, Venezuela Defense Minister General Vladimir Padrino called it "crazy" and showed America had "dropped its mask" in terms of wanting to attack his country.
The rest of Latin America -- even countries that condemn President Nicolas Maduro's attacks on Venezuela's democratic institutions -- have strongly rejected the threat.
China, which is owed billions in debt by Venezuela, also spoke out against foreign interference in other countries.
Colombian President Juan Manuel Santos had told Pence on arrival "that the possibility of a military intervention shouldn't even be considered."
Many Latin American countries have bitter memories of past US adventures in the region. Those include invasions, gunboat diplomacy and the propping up of military dictators.
Washington has already imposed unilateral sanctions on Maduro and nearly two dozen of his officials.
The sanctions were in response to their establishment of a new loyalist body, an all-powerful Constituent Assembly, that supersedes the legislature controlled by the opposition.
Trump's stated possibility of a US military operation looked likely to shadow Pence at every stop, eclipsing bilateral issues, especially trade, that he was raising along the way.
However the US defense officials at the Pentagon said on Monday they had not received any orders from the White House on a military option against Venezuela.
"I can't speculate what that is because we haven't been asked to provide any options," Pentagon spokesman Colonel Rob Manning said.
Maduro's regime has nevertheless seized on Trump's threat as proof of its claim that the United States wants to topple the current leftist government to get its hands on Venezuela's oil reserves, the largest in the world.
The Venezuelan opposition coalition on Sunday also rejected "the use of force, or the threat of applying such force, by whatever country against Venezuela."
The coalition is seeking to oust Maduro through early elections.
Venezuela's economy is heavily reliant on its oil exports. Shipments to the United States -- its biggest customer -- account for 40 percent of its crude production, but only eight percent of US oil imports.
The US sanctions so far have targeted individuals and not Venezuela's oil industry, which would have consequences for US refineries.