At least 29 children under the age of 15 were killed in the attack, according to the International Committee of the Red Cross.
@AdamjohnsonNYC I just saw MSNBC do a short segment on how USA back Saudi Arabia dropped a bomb on a school bus in Yemen.
The head of the humanitarian organisation's delegation in the country, Johannes Bruwer, later tweeted that "scores" had been killed and "even more injured, most under the age of 10".
Citing "local officials", the head of the global aid group's delegation in Yemen says that in total at least 50 people died and dozens more were injured.
"Today's attack in Saada was a legitimate military operation. and was carried out in accordance with worldwide humanitarian law", the coalition said in the Arabic-language statement carried by SPA.
"We call on the parties to take appropriate measures to protect civilians", she said.
A State Department spokeswoman expressed concern over the airstrike, and called for the Saudi-led coalition to investigate. In a statement released through the state-run Saudi Press Agency, Riyadh called the airstrike a "legitimate military action" conducted in accordance with global law.
Houthi spokesman Mohammed Abdul-Salam said the coalition had shown "clear disregard for civilian life" as the attack had targeted a crowded public place in the city.
Saudi Arabia shot down a missile fired by the Houthis on Wednesday, with debris killing a Yemeni man and wounding 11 others, the coalition said.
Colonel al-Maliki said the coalition will take all necessary actions against the criminal, terrorist acts of pro-Iranian Houthi militias, such as the recruitment and placement of children on battle fronts and "using them as tools to cover for their terrorist acts". Turki al-Malki said the attack was "a legitimate military action, conducted in conformity with worldwide humanitarian law".
Saudi Arabia and Arab allies have been fighting in Yemen for more than three years against the Iran-backed Houthis, who control much of northern Yemen including the capital Sanaa and drove a Saudi-backed government into exile in 2014.
The US, the United Kingdom and other Western powers have been providing arms and intelligence to the alliance in the course of the war, which has unleashed the world's worst humanitarian crisis in Yemen, according to the UN.
Norway Refugee Council Secretary-General Jan Egeland described Thursday's airstrike differently: "grotesque, shameful, indignant".
The Save the Children charity, quoting its staff, said that at the time of the attack the children were on a bus heading back to school "from a picnic when the driver stopped to get a drink".
Houthi media broadcast graphic footage appearing to show the bodies of children.
"We are certainly concerned about the reports that there was an attack that resulted in the deaths of civilians".
The coalition said Wednesday's attack brought the tally of rebel missiles launched since 2015, the year it joined the Yemeni government's fight against the rebels, to 165. Just last week at least 55 people died in the city during a particularly bloody exchange of fire in residential areas and outside a hospital.
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