The announcement led Venezuelan President Nicolás Maduro to call for rejecting "CIA-led coups" and "war in the Caribbean."
When asked if he had given the CIA authority to "eliminate" Maduro, Trump said, "It's ridiculous to ask me that question."
Trump also mentioned that he was considering carrying out ground attacks against Venezuelan cartels.
"We are certainly thinking about land now because we already have the sea well under control," Trump declared.
Following the latest maritime attack, the police in Trinidad and Tobago announced that they were investigating the possible deaths of two of their citizens after receiving reports from residents alerting that two compatriots were on the bombed vessel.
Experts question the legality of such attacks using lethal force in international waters against suspects who have not been detained or interrogated.
The Republican government is also facing opposition from the Democratic party in the Legislative branch, demanding explanations for these attacks.
Without directly referring to Trump's statements, Maduro called for rejecting a potential "CIA-led coup."
"No to war in the Caribbean, no to war in South America, yes to peace. No to regime change that reminds us so much of the failed endless wars in Afghanistan, Iran, Iraq, Libya. No to CIA-led coups," Maduro said.
"How long will CIA-led coups continue? Latin America does not want them, does not need them, and rejects them," he added in a broadcast that was mandatory on radio and television.