Saudi Arabian spokesman Col. "[ICRC] sending additional supplies to hospitals to cope with the influx".
A doctor treats children injured by the airstrike.
The International Committee of the Red Cross reported on Twitter that its medical team had received "the bodies of 29 children, all under 15 years old" and was treating "48 injured people, among them 30 children".
Al-Masirah, the TV station of the armed Houthi movement, said on its Twitter account that 39 people had been killed and 51 wounded.
The bus was travelling through Dahyan market in Saada province at the time. In a statement, Save the Children condemned the attacks and called for a "full, immediate and independent investigation into this and other recent attacks on civilians and civilian infrastructure, including schools and hospitals".
Both the United Nations chief and the US State Department called for investigations into the strike.
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The United States and other Western powers provide arms and intelligence to the alliance, and human rights groups have criticised them over coalition air strikes that have killed hundreds of civilians at hospitals, schools and markets.
The ICRC stressed that "under worldwide humanitarian law, civilians must be protected during conflict", while the secretary-general of the Norwegian Refugee Council Jan Egeland called it a "grotesque, shameful" attack that showed "blatant disregard for rules of war". Say: I want the State Dept to condemn the Saudis for bombing Yemeni children and I want the USA to stop selling weapons to Saudi Arabia.
The UN children's agency UNICEF said it was "very concerned with the initial reports of children being killed".
"Putting children in harm's way is horrific and deplorable and making them pay such a price is unacceptable". Video footage, which CBS News can't independently verify, appear to show the devastating aftermath.
He said the rebels have "ballistic missiles threatening our national security, Saudi cities and villages on the border. Causalities from today's attack continue to arrive", the Red Cross stated on August 9. He also accused the Houthis of recruiting children and using them in the battlefields to cover for their actions.
The coalition said Wednesday's projectile, fired toward the southwestern Saudi city of Jizan, was intercepted and destroyed but its fragments caused the casualties.
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.
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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.
Col. Al-Maliki stressed: "The Joint Forces Command of the Coalition will take all deterrent measures against such barbaric, frivolous launches in conformity with the global humanitarian law, and those who support these terrorist crimes will be held accountable for their actions".
ICRC said one of the hospitals it supports was treating the wounded.
The coalition denied responsibility for those attacks.
Aid agency CARE International noted that Thursday's strike came a week after the Hodeida bombardment. Just one week ago, an air raid in Hodeidah seaport claimed the lives of 55 civilians.
"It's hard to believe we live in a world where children should live in fear of such attacks, yet here we are", she added.
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