Dozens of students were returning from a summer camp when their driver paused to grab a something at a market in Yemen's Saada province.
Most of the children were inside the bus when the airstrike hit, according to a medic, Yahya al-Hadi.
The International Committee for the Red Cross says a local hospital received 29 bodies, predominantly of children younger than 15.
On its Twitter feed, Saudi-funded Al-Arabiya TV quoted a senior official who said the coalition was probing "collateral damage" from the strike.
Save the Children described the incident as "horrific", and called for a full, immediate and independent investigation into recent attacks on civilians and civilian infrastructure.
He said this made the attack a "legitimate military action in accordance with global humanitarian law". "The Secretary-General emphasizes that all parties must take constant care to spare civilians and civilian objects in the conduct of military operations".
"He call for an independent and prompt investigation into this incident".
Alarmed by the rise of a group they saw as an Iranian proxy, the UAE, Saudi Arabia and seven other Arab states intervened in an attempt to restore the government.
Col. Al-Maliki affirmed that the leaders and militants responsible for launching ballistic missiles and targeting civilians would be held accountable under the Coalition's efforts to prevent terrorist elements from compromising regional and global security. Fragments from a missile launched at the Jizan Industrial City in southern Saudi Arabia late on Wednesday, killed one Yemeni civilian and wounded 11, Saudi state media said earlier on Thursday. Turki al-Malki was defiant about the attack on the busload of children, saying it was retaliation for a missile strike from the rebel Houthis.
Saudi Arabia and Sunni Muslim allies have been fighting in Yemen for more than three years against the Houthis, who control much of north Yemen including the capital Sanaa and drove the government into exile in 2014.
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American support for the Saudi attacks in Yemen began under President Barack Obama, and President Donald Trump has vigorously continued the policy and ramped up munitions sales to the US ally.
"Grotesque, shameful, indignant. Blatant disregard for rules of war when bus carrying innocent school children is fair game for attack", Jan Egeland, head of the Norwegian Refugee Council, said in a Twitter post. Some shell-shocked boys are seen coming to, their faces bloodied and limbs charred.
The coalition faces widespread worldwide criticism for its airstrikes in Yemen that kill civilians.
The United Nations chief and the US State Department both called for the strike in Dahyan market to be investigated.
A week ago, at least 55 civilians were killed and 170 others wounded in a series of attacks on the rebel-held Red Sea port city of Hudaydah.
That was the toll at just one hospital.
Exact splits between children and people who were shopping at the market is not yet clear.
The vehicle was stationary when the attack happened, it said. "This doesn't have to be their reality though".
"The question now is whether it will also be a turning point - the moment that must finally push the warring parties, UN Security Council and global community to do what's right for children and bring an end to this conflict".