Trump said via Twitter that if Cuban troops and militia do not cease their operations in support of Venezuela immediately, Cuba would suffer "a full and complete embargo" as well as "highest-level sanctions."

Washington has repeatedly alleged that Havana has thousands of intelligence and security forces in Venezuela to shore up the government of President Nicolas Maduro, which Washington is openly seeking to oust from power.

Cuban Foreign Minister Bruno Rodriguez immediately responded via Twitter, saying "there are no Cuban troops in Venezuela; nor are there any Cubans taking part in military or security operations there."

Rodriguez said Cuba had only sent medical staff to Venezuela for humanitarian missions.

"I strongly reject Trump's total blockade threat," he added.

Currently, around 20,000 Cubans, mostly doctors and healthcare workers, work in Venezuela as part of a cooperation agreement that dates back to 2000, according to the Cuban government.

U.S.-Cuba ties have deteriorated under Trump, who has rolled back the detente initiated by his predecessor, Barack Obama.

The White House earlier this month announced a new round of punitive measures against Havana. Washington also announced a cap on remittances to the island and restrictions on non-family-related travels, a move that could affect American cruise companies and airlines that sail or fly to the island.