The bus was travelling through Dahyan market in Saada province at the time. Additionally, when asked by CNN about children killed in the incident, he said "Houthis are recruiting kids, ... why are the Houthi taking kids to the battlefield?"
Reporters at the scene said it was unclear why the bus was targeted, noting that there are no military installations anywhere near the market.
The assault was the latest in a string of airstrikes to target civilians by an American-backed regional coalition led by Saudi Arabia and the United Arab Emirates.
Errant strikes have killed hundreds of civilians at hospitals, schools and markets.
Most of the children were inside the bus when the airstrike hit, according to a local medic, Yahya al-Hadi.
"Scores killed, even more injured, most under the age of 10", Johannes Bruwer, head of delegation for the ICRC in Yemen, said in a further Twitter post.
Yemen's Houthi-run Al Masirah TV said that some 50 civilians had been killed and over 70 wounded in an airstrike that hit a bus, a lot of them were reported to be young children.
What has been the reaction?
"We call on the parties to take appropriate measures to protect civilians", Nauert said.
The coalition said the strike targeted the Iran-backed Huthi rebels responsible for a deadly missile attack on the Saudi city of Jizan on Wednesday.
UNICEF said in a statement that "many children were reportedly killed and injured" in the attack and that all of the children were reportedly under the age of 15. The rebels control much of northern Yemen, including the capital, Sanaa.
Sen. Chris Murphy (D-Conn.), an outspoken critic of the United States' support for the Saudi coalition, expressed fury over the attack and demanded once again that lawmakers end their complicity in the war.
The statement, carried by the official Saudi Press Agency, also said the missile was launched "deliberately to target residential and populated areas". We hope that all belligerents get to the peace table and start negotiating an end to this awful war.
Yemen has been devastated by a conflict that escalated in early 2015, when the Houthis seized control of much of the west of the country and forced President Abdrabbuh Mansour Hadi to flee overseas.
The devastating war in Yemen has been in progress for four years. A Saudi Arabian blockade has contributed to starvation and disease while a United Nations report found the Saudi-led bombing campaign - carried out with USA support - has hit schools, even weddings.
As many as 50 people were reported dead after the attack, with another 77 injured.
The fighting and a partial blockade by the coalition has also left 22 million people in need of humanitarian aid, created the world's largest food security emergency, and led to a cholera outbreak that is thought to have affected a million people.