Trump also warned Iran, the Houthis' main backer, that it needed to immediately halt support to the group. He said if Iran threatened the United States "America will hold you fully accountable and, we won’t be nice about it!"
At least nine civilians were killed and nine injured in US strikes on Yemen's Sanaa, according to the Houthi-run health ministry.
Residents in Sanaa said the strikes hit a building in a stronghold of the militant Houthi group.
"The explosions were violent and shook the neighborhood like an earthquake. They terrified our women and children," one of the residents, who gave his name as Abdullah Yahia, said.
The Houthis launched more than 100 attacks targeting shipping from November 2023, saying they were in solidarity with Palestinians over Israel's war with Hamas in Gaza.
During that period, the group sank two vessels, seized another and killed at least four seafarers in an offensive that disrupted global shipping, forcing firms to re-route to longer and more expensive journeys around southern Africa.
The previous U.S. administration of President Joe Biden had sought to degrade the Houthis ability to attack vessels off its coast but limited the US actions.
US officials, speaking on condition of anonymity, say Trump has authorised a more aggressive approach, which appeared to match his rhetoric Saturday.
"The Houthi attack on American vessels will not be tolerated. We will use overwhelming lethal force until we have achieved our objective," Trump wrote.
The attack marks the first strikes to hit Yemen since the Gaza ceasefire deal took effect in January.
It also came a few days after the Houthis said they would resume attacks on Israeli ships passing through the Red and Arabian seas, the Bab al-Mandab Strait and the Gulf of Aden, ending a period of relative calm starting in January with the Gaza ceasefire.
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