The Western-backed alliance fighting the Iranian-aligned Houthi group in Yemen said in a statement that the air strikes targeted missile launchers used to attack the southern Saudi city of Jizan on Wednesday, killing a Yemeni civilian there.
There was no immediate comment from the coalition, which is led by Saudi Arabia and which is fighting to restore Yemen's internationally recognized government to power.
Footage provided by the rebels' Ansarullah Media Centre showed a number of wounded children lying two to a hospital bed, while in a separate shot medics tended to casualties in a crowded room. Turki al-Malki said the attack was "a legitimate military action, conducted in conformity with worldwide humanitarian law". "We call on the Saudi-led coalition to conduct a thorough and transparent investigation into the incident", State Department spokeswoman Heather Nauert told a press briefing.
The attack was also denounced by the United Nations children agency, UNICEF. The attack happened while the bus was stationary.
Sen. Chris Murphy (D-Conn.), an outspoken critic of the United States' support for the Saudi coalition, expressed fury over the attack and demanded once again that lawmakers end their complicity in the war.
"Putting children in harm's way is horrific and deplorable and making them pay such a price is unacceptable", she said.
In a statement Thursday, the Saudi-led coalition said the strike was a "legitimate military action to target elements that planned and carried out" an attack that targeted civilians in Jizan, a border city in southwest Saudi Arabia.
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He added that Guterres has urged an "independent and prompt" probe into the attack that killed at least 50 civilians, mainly children, and wounded 77 others at a market in Yemen's northwestern province of Sa'ada.
Nearly 10,000 people - two-thirds of them civilians - have been killed since the Houthi movement took control of much of the north of the country, including the capital Sanaa, in 2014, forcing President Abdrabbuh Mansour Hadi into exile in neighbouring Saudi Arabia. He said this made the attack a "legitimate military action in accordance with global humanitarian law".
It accused the Houthis of using children as human shields and said the strikes were carried out in accordance with worldwide humanitarian law.
The missile was sacked from the rebel-held Yemeni province of Amran towards the Saudi city of Jizan, the coalition said.
The coalition denied responsibility for those attacks.
"We are trying to get rid of the arms manifestations in the province, and to carry on the efforts exerted by the UAE to counter the terrorism groups in Yemen", Col Mohammed Salem Al Buhar, commander of the elite forces in Shabwa, told The National. Just one week ago, an air raid in Hodeidah seaport claimed the lives of 55 civilians.