The alliance says it does not intentionally target civilians and has set up a committee to probe alleged mass casualty air strikes, which has mostly cleared the coalition of any blame.
He added: "Launching ballistic missiles at densely-populated civilian areas is a direct breach of the principles of worldwide humanitarian law".
"The coalition will take all necessary measures against the terrorist, criminal acts of the terrorist Iranian-Houthi militia, such as recruiting child soldiers, throwing them in battlefields and using them as tools and covers to their terrorist acts", Col Al Malki said.
He stressed that the Houthi leaders and terrorist elements responsible for firing ballistic missiles and targeting civilians will be targeted as part of the coalition efforts to prevent terrorist elements from harming regional and worldwide security.
Among the dead were children on a school bus that had been traveling through Dahyan Market, located in Yemen's Saada province, at the time of the attack.
The health ministry run by the rebel Houthi movement said 43 people were killed.
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.
Houthi media broadcast gruesome footage appearing to show the dead bodies of children.
"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.
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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.
The Iran-backed rebels have in recent months ramped up missile attacks against Saudi Arabia, most of which are intercepted.
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.
Aid agency CARE International noted that Thursday's strike came a week after the Hodeida bombardment.
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 worldwide humanitarian law, and those who support these terrorist crimes will be held accountable for their actions".
The coalition, which also includes the United Arab Emirates, intervened in 2015 to try to restore the internationally recognised government after the rebels drove it out of the capital Sanaa.
The war in the impoverished country has left almost 10,000 people dead and unleashed what the United Nations describes as the world's worst humanitarian crisis. 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.
"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.
There was a horrifying attack Thursday in Yemen - a Middle Eastern country torn apart by a 3-year-old civil war.