Venezuela has appeared to slide toward a more volatile stage of unrest in recent days, with anti-government forces looting weapons from a military base after a new legislative body usurped the authority of the opposition-controlled congress.
"The people are suffering and they are dying. We have many options for Venezuela including a possible military option if necessary," Trump told reporters in an impromptu question and answer session.
The comments appeared to shock Caracas, with Venezuela's Defense Minister Vladimir Padrino calling the threat "an act of craziness."
The White House said Venezuelan President Nicolas Maduro requested a phone call with Trump on Friday, which the White House appeared to spurn, saying in a statement that Trump would gladly speak to Venezuela's leader when democracy was restored in that country.
Venezuelan authorities have long said U.S. officials were planning an invasion. A former military general told Reuters earlier this year that some anti-aircraft missiles had been placed along the country's coast for precisely that eventuality.
In Washington, the Pentagon said the U.S. military was ready to support efforts to protect U.S. citizens and America's national interests, but that insinuations by Caracas of a planned U.S. invasion were "baseless."
Asked if U.S. forces would lead an operation in Venezuela, Trump declined to provide details. "We don't talk about it but a military operation - a military option - is certainly something that we could pursue," he said.
Senator Ben Sasse of Nebraska, a member of the Senate Armed Services Committee, criticized Trump's new stance.