The strikes - which killed at least 31 people at the start of a campaign that one US official told Reuters might continue for weeks - are the biggest US military operation in the Middle East since President Donald Trump took office in January.
The Houthis' political bureau described the attacks as a "war crime".
"Our Yemeni armed forces are fully prepared to respond to escalation with escalation," it said in a statement on Sunday.
Trump also warned Iran, the Houthis' main backer, that it needed to end support for the group immediately. He said if Iran threatened the United States, "America will hold you fully accountable and, we won't be nice about it!"
In response, the top commander of Iran's Revolutionary Guards said the Houthis took their own strategic and operational decisions and Tehran would react decisively to any action against it.
"We warn our enemies that Iran will respond decisively and destructively if they take their threats into action," Hossein Salami told state media.
Russian Foreign Minister Sergei Lavrov called US Secretary of State Marco Rubio to urge an "immediate cessation of the use of force and the importance for all sides to engage in political dialogue," Russia's foreign ministry said on Sunday.
However, Rubio told the CBS News Face the Nation Sunday program the strikes would continue until the Houthis no longer had the capability to attack global shipping and the US Navy.
Most of the 31 people confirmed killed in the US strikes were women and children, Anees al-Asbahi, spokesperson for the Houthi-run health ministry said in an updated toll on Sunday. More than 100 were injured in the neighbourhood known to host members of the Houthi leadership.
Strikes also targeted Houthi military sites in Yemen's southwestern city of Taiz and a power station in the town of Dahyan in Saada which led to a power cut.
The Houthis, an armed movement that took control of most of Yemen over the past decade, said last week they would resume attacks on Israeli ships passing through Red Sea shipping lanes off Yemen if Israel did not lift a block on aid into Gaza.
The Houthis had launched scores of attacks targeting shipping from November 2023, saying they were in solidarity with Palestinians over Israel's war with Hamas in Gaza.
The group has not launched new strikes on Red Sea shipping since it halted attacks when Israel and Hamas agreed to a ceasefire in Gaza in January.
US officials, speaking on condition of anonymity, say Trump has authorised a more aggressive approach.
"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!" Trump posted late Saturday on his Truth Social platform.
The US military's Central Command, which oversees troops in the Middle East, described Saturday's strikes as the start of a large-scale operation across Yemen.
"Houthi attacks on American ships & aircraft (and our troops!) will not be tolerated; and Iran, their benefactor, is on notice," Defense Secretary Pete Hegseth wrote on X.
Iran's foreign ministry condemned strikes on Yemen as a "gross violation of the principles of the United Nations Charter and the fundamental rules of international law".
The Lebanese armed group Hezbollah, also backed by Iran, expressed solidarity with the Houthis, calling it "barbaric aggression ... and a flagrant violation of international law".
