The Western-backed alliance fighting the Iranian-aligned Houthi group in Yemen said the air strikes targeted missile launchers, killing a Yemeni civilian there, a statement carried by the state news agency SPA said.
It accused the Houthis of using children as human shields.
"Today's attack in Saada was a legitimate military operation ... and was carried out in accordance with international humanitarian law," the Arabic-language statement said.
The ICRC said one attack hit the bus driving children in Dahyan market, in northern Saada, adding hospitals there had received dozens of dead and wounded.
It was unclear how many children were killed and how many air strikes were carried out in the area, in northern Yemen, near the border with Saudi Arabia.
Abdul-Ghani Nayeb, head of a health department in Saada told Reuters that the death toll rose to 43, with 61 wounded.
"Scores killed, even more injured, most under the age of 10," Johannes Bruwer, head of delegation for the ICRC in Yemen, said in a twitter post.
Saudi Arabia and Sunni Muslim allies have been fighting in Yemen for more than three years against the Houthis.
It has launched thousands of air strikes in a campaign to restore the internationally recognized government of President Abdrabbuh Mansour Hadi. Errant strikes have killed hundreds of civilians at hospitals, schools and markets.
The military alliance says it does not target civilians and has set up an investigation committee into alleged mass casualty air strikes which have mostly cleared the coalition of any blame.