The children were travelling on a bus that was hit at a market in Dahyan, in the northern province of Saada.
The U.S. State Department called on the Saudi-led coalition "to conduct a thorough and transparent investigation into the incident", spokeswoman Heather Nauert said.
Yemen is the poorest country in the Arabian peninsula, and the United Nations says the war has created the world's most urgent humanitarian disaster, with millions of people totally dependent on aid and at risk of starvation if supply lines are cut.
The U.S. said it was not involved in Thursday's assault. "The question now is whether it will be a turning point - the moment that must finally push the warring parties, U.N. Security Council and global community to do what is right for children and bring an end to this conflict". Despite our repeated calls for respect of worldwide humanitarian law, parties to the conflict in Yemen have acted with utter disregard.
Chaos on the scene means confirming the number of dead and injured at this early stage has been hard.
Video from Houthi run Al-Masirah TV appears to show several children who lost limbs in the attack.
The International Committee for the Red Cross says a local hospital received 29 bodies, predominantly of children younger than 15. The hospital also received 48 wounded people, among them 30 children.
"We have seen the images of children who died", the Dutch deputy ambassador Lise Gregoire-van Haaren told reporters. Verification is still ongoing and the charity says the figure could rise.
Yemen has become the world's worst humanitarian crisis, with more than 22.2 million people in need of assistance.
A UNICEF-supported water station and sanitation centre in Hodeida which provide families with access to clean water and help prevent another outbreak of cholera were attacked and seriously damaged in recent weeks.
The Western-backed alliance fighting the Iranian-aligned Houthi group in Yemen said its actions were legitimate, insisting it never deliberately targets civilians.
The alliance said the strikes had targeted missile launchers used to attack the Saudi city Jizan on Wednesday, killing a Yemeni civilian there.
"Today's attack in Saada was a legitimate military operation. and was carried out in accordance with global humanitarian law", the coalition said in the Arabic-language statement carried by SPA.
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.
Also on Friday, scores of Saudi-backed Yemeni militiamen loyal to resigned president Abd Rabbuh Mansur Hadi were killed and injured when Yemeni army soldiers launched a salvo of Katyusha rockets and artillery rounds at the Alab border crossing in Saudi Arabia's border region of Asir.
In a statement after Thursday's airstrike, United Nations chief António Guterres urged Yemen's warring parties to take "constant care to spare civilians" during military operations and also called for an "independent and prompt investigation".
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It would also be nice to see a more competitive side to the sport, which usually sees one side dominate the entire season. The team is looking at Charles Leclerc from Ferrari, Marcus Ericsson or Antonio Giovinazzi who is a reserve for Ferrari.