The International Committee of the Red Cross (ICRC) said a hospital it supported in Saada had received dozens of casualties on Thursday after the attack.
The attack on Jazan was the second ballistic missile fired at Saudi Arabia by the Iran-backed rebels this week. Reuters reported that the militants have fired dozens of missiles into the kingdom in recent months, often intercepted by Saudi forces.
"This is yet another example of the blatant violations of global humanitarian law that we have seen in Yemen over the past three years-from indiscriminate and disproportionate attacks on civilians, denial of access to humanitarian aid and the use of starvation as a weapon of war-it's the people of Yemen, not the warring parties, who are paying the ultimate price", said Sylvia Ghaly, director of advocacy in Yemen for Save the Children.
While the Saudi-led coalition admitted to carrying out the attack, they called it a "legitimate military action" that targeted the Iran-backed Houthis, and accused the rebels of using children as human shields.
Saudi Arabia and Sunni Muslim allies intervened in Yemen's war in 2015 against the Houthis, who control the most populous areas of Yemen, including the capital Sanaa, and drove the internationally recognized government into exile in 2014.
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".
"Our support to the coalition consists of aerial refueling and intelligence support to assist our partners in securing their borders from cross-border attacks from the Houthis". Three civilians were killed by a Houthi missile fired at Jazan in June.
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The Saudi government issued a statement on August 9 and described the strike as "a legitimate military action" and was "conducted in conformity with the global humanitarian law".
Investigations by the United Nations and the USA have found evidence that the missiles fired by the Houthis were supplied by Tehran.
Media captionThe conflict in Yemen has been raging for years - but what is it all about? "Spare the Yemeni people more death and misery".
It was not immediately clear whether the bus was the target of airstrikes, but coalition spokesman Col.
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. We urge all parties to agree to an immediate cessation of hostilities, return to the negotiation table to commit to a ceasefire and cooperate with the UN Special Envoy Martin Griffiths.
"The main goal of the meeting is to have the opportunity to consult with Yemeni social and political figures who possess a unique knowledge of the Yemeni society", said Mr Griffiths, who chaired the meeting.