The warning came amid reports of armed militias.
Deposed Venezuelan President Nicolás Maduro and his wife appeared in a federal court in New York City on Monday, following their capture by U.S. forces over the weekend in a military operation in the Venezuelan capital of Caracas.
Following the operation, President Donald Trump said that the U.S. would "run" Venezuela for an unspecified "period of time."
Venezuelan Vice President Delcy Rodriguez has been sworn in as interim leader to lead the country after what the Venezuelan Supreme Court described as Maduro's "kidnapping."
Trump was asked about the possibility that the U.S. "ends up administering Venezuela for years."
"Well, you know, it won't cost us anything, because the money coming out of the ground is very substantial," the president said.
"We're going to get reimbursed for everything that we spend. So it's going to be, it's going to be a very important," he added.
Trump said that American oil companies are going to restart operations in Venezuela.
"As everyone knows, the oil business in Venezuela has been a bust, a total bust, for a long period of time. They were pumping almost nothing, by comparison to what they could have been pumping and what could have taken place," Trump said.
"We're going to have our very large United States oil companies, the biggest anywhere in the world, go in, spend billions of dollars, fix the badly broken infrastructure, the oil infrastructure, and start making money for the country," Trump added.
When asked by a reporter how long the U.S. plans on staying in Venezuela and how soon he would like the country to hold elections, Trump responded, "I'd like to do it quickly, but it takes a period of time."
The president cited infrastructure improvements, contending that it was "old, rotted."
Gen. Dan Caine, chairman of the Joint Chiefs of Staff, said the operation in Venezuela was known as Operation Absolute Resolve and involved more than 150 aircraft across the Western Hemisphere.
Caine said it was the "culmination of months of planning and rehearsal" adding that the operation could only have been conducted by the U.S. military.
"Maduro and his wife, both indicted, gave up and were taken into custody by the Department of Justice, assisted by our incredible U.S. military with professionalism and precision, with no loss of U.S. life," Caine said.
