Speaking before the strike, US Secretary of State Marco Rubio said the United States expected to conclude military operations within weeks but the Houthis said they would continue their operations until the "aggression" on all fronts ended.
Iranian President Masoud Pezeshkian spoke to Pakistani Prime Minister Shehbaz Sharif, whose government hosts a meeting with the Turkish and Saudi foreign ministers on Sunday, to seek to ease regional tensions.
But there is no sign of an immediate diplomatic breakthrough and the war, launched with US and Israeli strikes on Iran on February 28, has spread across the Middle East, killing thousands and hitting the world economy with the biggest-ever disruption to global energy supplies.
On Saturday, Israel said it had carried out a wave of attacks on Tehran, targeting what the military said were infrastructure sites belonging to Iran's government.
It also hit targets in Lebanon, where it has resumed its war against Iran-backed Hezbollah, killing three Lebanese journalists in a strike on a media vehicle, Lebanon's al-Manar TV reported, as well as a Lebanese soldier.
Iran also kept up attacks after hitting an air base in Saudi Arabia on Friday and wounding 12 US military personnel, two of them seriously, in one of the most serious breaches of US air defences so far.
Kuwait International Airport was targeted by multiple drone attacks on Saturday that caused significant damage to its radar system but resulted in no casualties, state news agency KUNA reported, citing the country's Civil Aviation Authority.
The authority's spokesperson later said the attacks were carried out by Iran, its proxies and the armed factions it supports.
Kuwait's fire department, meanwhile, said a fire that broke out in fuel tanks at the airport on Wednesday following a previous drone attack had been extinguished after operations lasting 58 consecutive hours, KUNA reported on Saturday.
Israel, which regularly faced missile attacks from the Houthis before the war, confirmed a missile had been fired at it from Yemen.
There were no reports of casualties or damage.
Israel has targeted Iran's nuclear infrastructure and the head of Russia's state nuclear corporation Rosatom, which has removed staff from the Bushehr nuclear power plant on the Gulf coast, said the attacks threatened nuclear safety.
Pezeshkian said Iran would "retaliate strongly if our infrastructure or economic centres are targeted".
"To the countries of the region: If you want development and security, don't let our enemies run the war from your lands," he said.
Pakistan, Egypt and Turkey have been relaying messages between the warring sides although Iran has said it has not been negotiating with the United States.
Two people familiar with the back-channel efforts expressed doubt that direct talks would take place soon.
Missile attacks were also reported in the United Arab Emirates and Bahrain on Saturday, and fires were reported after a missile was intercepted near Abu Dhabi's Khalifa Port, one of the Gulf's main deepwater container ports.
At least five people were killed in a US-Israeli attack on a residential unit in Iran's northwestern city of Zanjan, Iranian media reported early on Saturday.
The Iran University of Science and Technology in Tehran was struck, media reported.
An Iranian missile struck the Israeli village of Eshtaol, near Jerusalem.
Seven people were hospitalised, Israel's ambulance service said.
