"The air strikes targeted a bus full of school students in the middle of Dahyan market in Saada province while they were going to their school", the official said.
The Saudi-led coalition is fighting to defeat Houthi rebels who expelled the Yemeni government from the capital and took control of vast swathes of the country.
Footage from the scene, in the area of northern Yemen that is the heartland of the Houthi rebels fighting the recognised government, showed children as young as six being pulled from the wreckage.
The coalition acknowledged carrying out a "legitimate military action", but spokesman Turki al-Maliki told AFP claims that children were inside the bus were "misleading", adding that the bus carried "Huthi combatants". The Saudi coalition has been at war with the Houthis since March 2015.
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However, a recent review of airstrikes by the United Nations found that "measures taken by the Saudi Arabia-led coalition in its targeting process to minimize child casualties, if any, remain largely ineffective".
Doctors Without Borders (MSF) said "civilians continue to pay the highest price after three years of war in Yemen, thousands of them have been killed, injured or maimed".
The school bus was hit as it was driving through a market in the rebel-held province of Saada, according to the Houthi-run Al-Masirah TV.
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The missile was sacked from Amran province in northern Yemen on Wednesday night, the coalition said in a statement published by the Saudi Press Agency. The military action in Saada province, which lies between Amran and Saudi Arabia, was in line with global humanitarian law, he said.
There was no immediate comment from the Houthis in response to the coalition allegations. The coalition denied that it had carried out air strikes in the area, and blamed the deaths on rebel mortar fire.
"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.
"This latest air strike, only a week after the attacks on Hodeida city, demonstrates a continued disregard for human life and suffering", said Johan Mooij, the agency's country director in Yemen.
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Impoverished Yemen, on the southern tip of the Arabian Peninsula, is now in the world's worst humanitarian crisis, with more than 22.2 million people in need of assistance. "Parties to the conflict and those who have influence over them, including Security Council members, can and should choose to end this catastrophe for the sake of Yemen's children".