Trump on Saturday also warned Iran, the Houthis' main backer, that it must immediately stop supporting the group.Â
The US was carrying out airstrikes against Houthi bases, leaders and missile defence sites in order to protect US shipping and restore freedom of navigation, Trump wrote on his Truth Social platform.
"They have waged an unrelenting campaign of piracy, violence, and terrorism against American, and other, ships, aircraft, and drones," Trump wrote.
Tehran should not threaten the American people, its president or global shipping routes, Trump said.
If Iran does, it should "BEWARE because America will hold you fully accountable, and we won't be nice about it!" he added.
The Houthi militia said late on Saturday that US-British strikes had hit areas north Sana'a.
The Houthi-affiliated television station al-Masirah said that "an American-British aggression targeted a residential neighbourhood in the Shu'ub district, north of the capital, Sana'a, with raids".
Thirteen civilians were killed and nine others were injured in the airstrikes, a spokesman from Yemen's Ministry of Health and Environment told Lebanese broadcaster Al Mayadeen.
The SABA news agency cited the Yemeni ministry as condemning the targeting of civilians and civilian objects, which it said constitutes a full-fledged war crime and a flagrant violation of all international laws and conventions.
"We affirm the right of Yemen and its armed forces to respond appropriately to the arrogance, intransigence, terrorism, and American-British aggression," the Yemeni parliament said, according to al-Masirah.
The Houthi militia meanwhile in response to the strikes said that "the aggression will not go unanswered, and our armed forces are fully prepared to respond to escalation with escalation".
Residents in Sanaa said the strikes hit a building in a stronghold of the militant Houthi group.
"The explosions were violent and shook the neighbourhood like an earthquake. They terrified our women and children," one of the residents, who gave his name as Abdullah Yahia, told Reuters.
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 US 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.
"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.
