Defense Secretary Pete Hegseth warned in an appearance on “Fox & Friends” on Wednesday that a deadly U.S. military strike on a boat officials said was carrying drugs in the Caribbean was the start of a campaign against Venezuelan cartels that President Trump has blamed for bringing fentanyl into the United States.

Mr. Hegseth said officials “knew exactly who was in that boat” and “exactly what they were doing,” although he did not offer evidence. “President Trump is willing to go on offense in ways that others have not seen,” he added.

Mr. Trump shared more details about the strike in a Truth Social post on Tuesday afternoon.

“Earlier this morning, on my Orders, U.S. Military Forces conducted a kinetic strike against positively identified Tren de Aragua Narco terrorists,” Mr. Trump wrote. He said the strike “occurred while the terrorists were at sea in International waters transporting illegal narcotics, heading to the United States.”

The strike, which the president said killed 11 people, was an astonishing departure from traditional drug interdiction efforts and came amid a major buildup of U.S. naval forces outside Venezuela’s waters, which Mr. Hegseth described as “a clear demonstration of military might.”

The administration has also labeled Venezuela’s president, Nicolás Maduro, a terrorist cartel leader. Mr. Maduro, Mr. Hegseth said, “is running effectively as a kingpin of a drug narco state.”

Mr. Trump signed a still-secret directive in July instructing the Pentagon to use military force against some Latin American drug cartels that his administration has labeled “terrorist” organizations. Around the same time, the administration declared that a Venezuelan criminal group was a terrorist organization and that Mr. Maduro was its leader, while calling his government illegitimate.

Helene Cooper, Edward Wong and Alan Feuer contributed reporting.