The White House said on Monday that US Defense Secretary Pete Hegseth authorised an admiral to conduct multiple strikes on a vessel from Venezuela allegedly carrying illegal narcotics in September.

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.

Hegseth had vehemently denied that he ordered a second strike. He called such reports "fabricated, inflammatory and derogatory" on social media.

Trump said he would look into the matter, but he believed Hegseth "100 percent" when he said he had not ordered one.

But White House spokeswoman Karoline Leavitt said on Monday that 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 defense" 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 lawmakers 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.

US troops have carried out at least 21 strikes on alleged drug boats in the Caribbean and Pacific since September, killing at least 83 people as Trump escalates a military buildup against President Nicolas Maduro's government.

In November, Senate Republicans blocked a resolution that would have prevented Trump from attacking Venezuelan territory without congressional authorisation.

Only two of Trump's Republicans joined Democrats in backing the measure, in a show of the party's support for the military buildup in the southern Caribbean.

In October, Senate Republicans blocked a resolution that would have stopped the boat strikes. (Reuters)