Saudi Arabia and allies have been fighting in Yemen for more than three years against the Iran-backed Houthis, who control much of northern Yemen including the capital Sanaa and drove a Saudi-backed government into exile in 2014.
The strike by the Western-backed alliance, in which at least 40 children are said to have been killed, outraged human rights groups and was strongly condemned by United Nations officials.
He said: "No there were not children on the bus".
Save the Children said it "condemns this horrific attack and is calling for a full, immediate, and independent investigation into this and other recent attacks on civilians and civilian infrastructure".
"This latest air strike, only a week after the attacks on Hodeida city, demonstrates a continued disregard for human life and suffering", said Johan Mooij, the agency's country director in Yemen.
The World Health Organization (WHO) representative in Yemen, Nevio Zagaria, said it has deployed emergency supplies.
He insisted the strike was aimed at a "legitimate target". "The attack on civilians is not acceptable".
State Department spokeswoman Heather Nauert said the U.S.is concerned about the incident and calls on all parties to take appropriate measures to protect civilians in the area, during a briefing Thursday.
Asked if the White House and the State Department were offering differing views, the spokesperson said: "We have the same position".
In this file picture, Yemeni forces prepare to launch a domestically-manufactured Badr-1 ballistic missile at a military site in Saudi Arabia.
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But some evacuees have complained of being ignored or experiencing long delays for supplies to arrive at shelters. It comes just four days after a massive 6.9 magnitude quake shook the region on Sunday, killing 350 people.
Hussain al Bukhaiti joins TRT World from Sanaa, and explains why the civilian casualty count of the latest Saudi air strike was so high.
It was not immediately clear whether the bus was the target of the air strike, but coalition spokesman Col Turki al-Malki said the attack was "a legitimate military action, conducted in conformity with global humanitarian law".
"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.
The coalition said Wednesday's attack brought the tally of rebel missiles launched since 2015, the year it joined the Yemeni government's fight against the rebels, to 165.
Coalition spokesman Turki al-Maliki told AFP that claims by aid organisations that children were inside the bus were "misleading", and that "the elements inside the bus were Huthi combatants". The coalition said it had intercepted and destroyed the missile but its fragments killed one person and wounded 11 others in Saudi's southwestern border region of Jizan.
The Houthis have however barred without explanation the head of the U.N.'s human rights office in Yemen from returning to the country, a United Nations spokeswoman said on Friday.
Al Masirah, the TV station of the armed Houthi movement, said on its Twitter account that 39 people had been killed and 51 wounded.
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.
Some 15,000 Yemenis have been killed and thousands more injured since the onset of the Saudi-led aggression on Yemen in March 2015.