The Washington Post had reported that a second strike was ordered to kill two survivors from the initial strike and to comply with an order by Hegseth that everyone be killed.
President Donald Trump said on Sunday that he would not have wanted a second strike on the boat and said Hegseth denied giving such an order.
But White House spokeswoman Karoline Leavitt said Hegseth had authorised Admiral Frank Bradley to conduct the strikes on September 2.
"Secretary Hegseth authorised Admiral Bradley to conduct these kinetic strikes. Admiral Bradley worked well within his authority and the law directing the engagement to ensure the boat was destroyed and the threat to the United States of America was eliminated," Leavitt said.
Leavitt said the strike was conducted in "self defence" to protect US interests, took place in international waters and was in line with the law of armed conflict.
"This administration has designated these narco terrorists as foreign terrorist organisations," Leavitt said.
Starting in September, the US military has carried out at least 19 strikes against suspected drug vessels in the Caribbean and off the Pacific coasts of Latin America, killing at least 76 people.
Critics have questioned the legality of the strikes, and both Republican and Democratic politicians have pledged to look into them.
International humanitarian law prohibits attacks on incapacitated combatants. The Defence Department's Law of War Manual states that shipwrecked persons cannot be knowingly attacked and must receive medical care unless they act with hostility or attempt escape.
George Washington University law professor Laura Dickinson said most legal experts do not believe the boat strikes qualify as armed conflict, so lethal force would only be allowed as a last resort.
On X, Hegseth defended Bradley, calling him "an American hero" and saying he has his "100% support."
Hegseth said he stands by Bradley's combat decisions "on the September 2 mission and all others since."
Trump on Monday discussed with top advisers the pressure campaign against Venezuela, among other topics, a senior US official said.
Trump has flagged the possibility of US military intervention in Venezuela. On Saturday, he said the airspace above and surrounding Venezuela should be considered "closed in its entirety," but gave no further details, stirring anxiety and confusion in Caracas.
Trump confirmed on Sunday that he had spoken to Venezuelan President Nicolas Maduro, whom the US considers an illegitimate leader, but the US president declined to provide details of the conversation.
The Trump administration has been weighing options to combat what it has portrayed as Maduro's role in supplying illegal drugs that have killed Americans. Maduro has denied having any links to the illegal drug trade.
