The New York Times first reported the classified directive, citing US officials familiar with the decision.
Trump said he authorised the action because large amounts of drugs were entering the United States from Venezuela, much of it trafficked by sea.
"We are looking at land now, because we've got the sea very well under control," he said.
Trump was asked why he did not have the Coast Guard stop suspected drug trafficking boats, which has been US practice for decades. The president called such efforts "politically correct" and said they had not worked.
"I think Venezuela is feeling heat," Trump said, although he declined to answer when asked if the CIA has the authority to execute Maduro.
Trump also accused Venezuela of releasing large numbers of prisoners, including individuals from mental health facilities, into the United States, although he did not specify which border they were crossing.
Neither Maduro's Information Ministry nor press representatives for opposition leader Maria Corina Machado immediately responded to requests for comment on Trump's remarks.
