The Western-backed alliance fighting the Iranian-aligned Houthi group in Yemen said in a statement that the air strikes targeted missile launchers.
Saudi-led coalition air strikes on Thursday killed at least 50 people, including 29 children travelling on a bus through a market, in Yemen's Saada province, a Yemeni health official and the International Committee of the Red Cross (ICRC) said.
The Western-backed alliance fighting the Iranian-aligned Houthi group in Yemen said in a statement that the air strikes targeted missile launchers used to attack the southern Saudi city of 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 international humanitarian law," the coalition said in the Arabic-language statement carried by Saudi Press Agency.
UN Secretary-General Antonio Guterres on Thursday condemned the air strikes and called for an "independent and prompt investigation."
Middle East director for UN Children's Fund (UNICEF), Geert Cappelaere, said he is "simply horrified" by the loss of children's lives and urged the warring sides to "stop this brutal war".
Houthi spokesman Mohammed Abdul Salam said the coalition showed "clear disregard for civilian life" as the attack had targeted a crowded public place in the city.
The ICRC said a strike hit the bus driving children in Dahyan market, in northern Saada.
"Our shops were open and shoppers were walking around as usual. All of those who died were residents, children and shop owners," witness Moussa Abdullah, who was being treated in hospital for wounds, said.
Abdul Ghani Sareeh, from Saada health department, said, "A bus carrying children was targeted today while they were coming from summer school resulting in 43 martyrs and almost 63 wounded."
White plastic body bags filled the floor of a room in the ICRC-supported hospital.
Injured children, bloodied, bandaged and screaming, lay on stretchers as doctors treated them, friends and relatives having carried some of them in their arms to be treated.
It was unclear how many of the 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.
Saudi Arabia and and its 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.
US and other Western powers provide arms and intelligence to the alliance, and human rights groups have criticised them over coalition air strikes that have killed hundreds of civilians at hospitals, schools and markets.
A US military spokeswoman said US forces were not involved in Thursday's air strike.
"Grotesque, shameful, indignant. Blatant disregard for rules of war when bus carrying innocent schoolchildren is fair game for attack," Jan Egeland, head of the Norwegian Refugee Council, said in a Twitter post.
The World Health Organization (WHO) representative in Yemen, Nevio Zagaria, said it has deployed emergency supplies. "I am extremely saddened by what happened in Saada ... The attack on civilians is not acceptable."
Red line crossed
The Saudi coalition 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.
"Targeting Saudis and residents in Saudi is a red line," coalition spokesman Turki al Malki told media.
US State Department spokeswoman Heather Nauert said the United States was concerned about reports of the air strikes and urged the Saudi-led coalition to "conduct a thorough and transparent investigation."
Separately, a White House National Security Council spokeswoman referred to "conflicting reports in global media" and said "we are waiting for an official assessment of what actually happened."
Asked if the White House and the State Department were offering differing views, the spokeswoman said: "We have the same position."
The Houthis have launched a series of missile strikes on the kingdom, including Riyadh, over the past year.
Saada, the main stronghold of the Houthis, has mainly come under air strikes from the coalition as the mountainous province makes battles hard for pro-government ground troops.
The Yemen war has killed more than 10,000 people, displaced more than 2 million and driven the country to the verge of famine, according to the United Nations.