The US has expanded its military presence in the Caribbean and carried out a series of lethal strikes on suspected drug-smuggling boats in international waters off Venezuela and Colombia, as part of what it calls is an anti-narcotics operation.
More than 80 people have been killed since early September.
The Trump administration says it is acting in self-defence by destroying boats carrying illicit drugs to the US.
In its report on Friday, The Washington Post wrote that Secretary Hegseth "gave a spoken directive" to "kill everybody" on board one such vessel, and a Special Operations commander overseeing the operation "ordered a second strike to comply with Hegseth's instructions".
Republican and Democrat lawmakers appearing on Sunday talk shows said they supported congressional reviews of US military strikes on vessels suspected of smuggling drugs in the Caribbean.
The leaders said they did not know whether The Washington Post's report was true, but they said attacking survivors of an initial missile strike presented major legal concerns.
"This rises to the level of a war crime if it's true," said Democrat Senator Tim Kaine on CBS Face the Nation.
Republican lawmaker Mike Turner said Congress did not have information that the follow-up strike had happened.
"Obviously if that occurred, that would be very serious, and I agree that that would be an illegal act," Turner, a former chairman of the Intelligence Committee, told CBS.
