Venezuela has appeared to slide towards 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.
Washington has slapped sanctions on President Nicolas Maduro and some of his allies, and branded him a "dictator" over his attempts to crush his country's opposition. Venezuela has, in turn, accused America of "imperialist aggression".
"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 later 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 US officials were planning an invasion.
A former military general told Reuters news agency 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 US military was ready to support efforts to protect US citizens and America's national interests, but that insinuations by Caracas of a planned US invasion were "baseless".
Senator Ben Sasse of Nebraska, a member of the Senate Armed Services Committee, criticised Trump's new stance.
"Congress obviously isn't authorising war in Venezuela," he said in a statement.
"Nicolas Maduro is a horrible human being, but Congress doesn't vote to spill Nebraskans' blood based on who the Executive lashes out at today."
The US military has not directly intervened in the region since a 1994-1995 operation that aimed to remove from Haiti a military government installed after a 1991 coup.