The coalition's statement ramps up tensions between the ultraconservative Sunni kingdom and its Shiite rival Iran, both of which have interests in Yemen's yearslong conflict. The bloodshed continued yesterday as an Islamic State-claimed militant attack in Aden killed at least 17 people.
In a statement, the coalition accused Iran of supplying Yemen's Houthi rebels and their allies with the missile launched on Saturday toward the Saudi capital's international airport.
The Saudi-led coalition's statement said the closures would be temporary and "take into account" the work of humanitarian and aid organisations. The war has claimed more than 10,000 lives and driven the Arab world's poorest country to the brink of famine.
The Saudi-led coalition launched a wave of airstrikes -- starting overnight and continuing until noon yesterday -- on the rebel-held capital, Sanaa, apparently in response to the ballistic missile.
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Saudi Arabia said it shot down the missile, with fragments landing in an uninhabited area north of the capital. The coalition threatened Iran with a possible retaliatory strike.
"Therefore, the coalition's command considers this a blatant act of military aggression by the Iranian regime, and could rise to be considered as an act of war against the kingdom of Saudi Arabia."
The statement added: "The coalition command also affirms that the kingdom reserves its right to respond to Iran in the appropriate time and manner."
There was no immediate response from Iran, though Iran's defence minister, Gen. Amir Hatami, earlier denied his country was involved in the launch.
President Donald Trump also was quick to blame Iran yesterday. "A shot was just taken by Iran, in my opinion, at Saudi Arabia. And our system knocked it down," Trump said, referring to the Patriot missile batteries Saudi Arabia purchased from the US.
Iran's powerful Revolutionary Guard chief, Maj. Gen. Mohammad Ali Jafari, said Iran can't transfer rockets to Yemen and stressed that the missiles were made there. He described Trump's comments as "lies."
Meanwhile in Aden, masked militants claimed by an Islamic State affiliate set off a large car bomb outside a security headquarters in Yemen's southern port city early yesterday, killing at least 17 people before storming the compound, officials said. Fighting continued well into the night.
Speaking on condition of anonymity because they were not authorised to brief reporters, the security officials said the militants placed snipers on the roof and gunned down most of the security forces inside.
Security forces backed by an Apache helicopter continued to fight for control of the installation after nightfall, chasing down militants in the surrounding structures and neighbourhood.
Some hostages were killed, they added, without providing specific figures. They said at least five soldiers were among the dead.