Errant strikes have killed hundreds of civilians at hospitals, schools and markets.
Aid agency CARE International noted that Thursday's strike came a week after the Hodeida bombardment.
"I was less than half a kilometre away and heard an explosion".
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.
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".
He accused the rebels of using children as "tools and covers for their terrorist acts".
"Targeting Saudis and residents in Saudi is a red line", coalition spokesman Turki al-Malki later told Al Arabiya TV. The Red Cross said most of the victims were under the age of 10.
"Air strikes usually target relievers, but this time they didn't", he said. "The air strikes often target civilians in Saada, so we appeal the worldwide community to intervene to stop the Saudis killing them". It also received 48 wounded, including 30 children. "Our non-combat support focuses on improving coalition processes and procedures, especially regarding compliance with the law of armed conflict and best practices for reducing the risk of civilian casualties", the statement added.
Citing "local officials", the head of the global aid group's delegation in Yemen says that in total at least 50 people died and dozens more were injured.
Houthi militants responsible for firing ballistic missiles and targeting civilians "will be held accountable", said the Saudi statement.
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Hariri later rescinded the resignation, widely believed to be orchestrated by Riyadh, and returned to Beirut. Countries in the Middle East are not exactly known for men supporting women in living their best lives.
Geert Cappelaere, the UN Children's Fund regional director in the Middle East and North Africa, said the children were "reportedly under the age of 15".
"I am watching with horror the images and videos coming from Saada in #Yemen and I have no words".
It was unclear how numerous dead in total were children and how many air strikes were carried out in the area, in northern Yemen, near the border with Saudi Arabia.
The Saudi-led military campaign was launched in support of Yemen's former Riyadh-friendly government and against its popular Houthi movement.
US State Department spokeswoman Heather Nauert said the United States did not have the "full details of what happened on the ground" but said "we're concerned about these reports".
But the International Committee of the Red Cross said the strike hit a bus filled with children in the Huthi stronghold of Saada, causing dozens of casualties.
The attack, the spokesperson said, was retaliation for a missile fired into Saudi Arabia Wednesday, killing one and injuring 11 more.
The coalition denied responsibility for those attacks.
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 recognised government into exile in 2014.
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