The Washington Post had reported that a second strike was ordered to take out two survivors from the initial strike and to comply with an order by Hegseth that everyone be killed.
President Donald Trump, who is holding a meeting about Venezuela with his national security team later in the day, 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.
"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.
Critics have questioned the legality of the strikes, and both Republican and Democratic politicians have pledged to look into them.
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 Trump 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.
Reuters has reported the options under US consideration include an attempt to overthrow Maduro, and that the US military is poised for a new phase of operations after a massive military build-up in the Caribbean and nearly three months of strikes on suspected drug boats off Venezuela's coast. Trump also has authorised covert CIA operations in the South American nation.
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