"In response to this aggression, the armed forces conducted a military operation... targeting the US aircraft carrier USS Harry Truman and its accompanying warships", the group said in a statement.
The Houthis said they had launched 18 missiles and a drone at the American ships.
There was no immediate comment from the United States about the claim.
Saturday's American attacks on the rebel-held capital Sanaa as well as Saada, Al-Bayda and Radaa killed at least 31 people and wounded 101, Houthi health ministry spokesperson Anis al-Asbahi said earlier.
"Most of whom were children and women", he said.
US officials on Sunday vowed further strikes until the Houthis stop attacking Red Sea shipping.
President Donald Trump said he had ordered Saturday night's strikes and threatened more if the rebel attacks continue.
Before Sunday's claimed attack on the carrier, the rebels had carried out no attacks in the Red Sea and Gulf of Aden since January 19, when a ceasefire began in the Gaza Strip.
On Tuesday, however, the Houthis said they would resume attacks on Israeli shipping.
'Overwhelming force'
US National Security Advisor Michael Waltz told ABC News that Saturday's strikes "targeted multiple Houthi leaders and took them out".
He told Fox News: "We just hit them with overwhelming force and put Iran on notice that enough is enough."
Pentagon chief Pete Hegseth vowed an "unrelenting" missile campaign until the Houthi attacks stop.
"I want to be very clear, this campaign is about freedom of navigation and restoring deterrence," Hegseth said in a televised Fox Business interview.
"The minute the Houthis say, 'We'll stop shooting at your ships, we'll stop shooting at your drones,' this campaign will end. But until then, it will be unrelenting."
CENTCOM, the US Central Command, said it had carried out a "large scale operation" against the Houthis.
Witnesses in Yemen said Sunday they were taken aback by the intensity of the attack.
Footage on Houthi media showed children, including a dazed girl with blackened legs wrapped in bandages, and a woman being treated in hospital.
One father of two, who gave his name as Ahmed, told AFP: "I've been living in Sanaa for 10 years, hearing shelling throughout the war. By God, I've never experienced anything like this before," he said.
Trump, posting on social media, vowed to "use overwhelming lethal force" to end the Houthi attacks, which the rebels say are in solidarity with Palestinians during the Gaza war.
"To all Houthi terrorists, YOUR TIME IS UP, AND YOUR ATTACKS MUST STOP, STARTING TODAY. IF THEY DON'T, HELL WILL RAIN DOWN UPON YOU LIKE NOTHING YOU HAVE EVER SEEN BEFORE!" he said.
"To Iran: Support for the Houthi terrorists must end IMMEDIATELY!" Trump added.
The Houthis, who had long complained of marginalisation, seized Sanaa in September 2014, forcing the government to flee south and leaving the rebels controlling large parts of Yemen.
A Saudi-led coalition in March 2015 began a military campaign against the Houthis that the Yemen Data Project, an independent tracker, said involved more than 25,000 air raids.
Iran's Foreign Minister Abbas Araghchi condemned the deaths in Saturday's US strikes and said Washington had "no authority" to dictate Tehran's foreign policy.
CENTCOM said "precision strikes" were launched to "defend American interests, deter enemies, and restore freedom of navigation".
'Fully prepared'
The Houthis' political bureau said its "forces are fully prepared to confront escalation with escalation".
They have launched scores of drone and missile attacks on ships in the two key waterways, and have previously targeted US warships.
Pentagon spokesman Sean Parnell said the Houthis had "attacked US warships 174 times and commercial vessels 145 times since 2023".
The Yemen Conflict Observatory database set up by ACLED, a non-profit monitor, shows 136 Houthi attacks against warships, commercial vessels, Israeli and other targets since October 19, 2023.
The campaign put a major strain on the vital trade route, which normally carries about 12 percent of world shipping traffic, forcing many companies to take a costly detour around southern Africa.
The Palestinian group Hamas, which has praised Houthi support, branded the US strikes "a stark violation of international law and an assault on the country's sovereignty and stability".
The head of Iran's Revolutionary Guards, Hossein Salami, said: "Iran will not wage war, but if anyone threatens, it will give appropriate, decisive and conclusive responses."
The United States had already launched several rounds of strikes on Houthi targets.
Israel has also struck Yemen, most recently in December, after Houthi missile fire towards Israeli territory.
Trump's administration this month reclassified the Houthis as a "foreign terrorist organisation", banning any US interaction with the group.
Fighting in Yemen's own war has largely been on hold since a 2022 ceasefire, but the promised peace process has stalled in the face of the Houthi attacks on Israel and Israel-linked shipping.
The war killed hundreds of thousands either directly or indirectly through causes such as disease, plunging Yemen into one of the world's worst humanitarian crises.
Short link: