The education of a further 3.7 million children at risk as teachers' salaries have not been paid in more than two years, UNICEF warns in a statement.
Dozens of people were wounded, including women and children, in the assault on Sanaa's residential centre.
Earlier this month, the US Congress had voted for the first time to invoke the War Powers Resolution to try to stop US involvement in a foreign conflict.
Save The Children, which supports the hospital, said four of those killed were children and two adults remain unaccounted for. The air strike came as Yemenis marked the fourth anniversary of a war which killed thousands and has starved the country.
Norwegian Refugee Council says sniper and explosive attacks have been growing despite an easing of air attacks amid a three-month-old truce in Hudaida, as the devastating conflict intensifies elsewhere.
Both sides in Yemen's devastating four-year war agreed to a series of confidence-building measures, including an exchange of thousands of prisoners.
The Kingdom of Saudi Arabia offered around $10,000 to families in Darfur, Sudan affected by the Sudanese civil war to send their children to fight in Yemen, the New York Times reported on Friday. The Saudi-led coalition has denied the accusations.
UN special envoy Martin Griffiths urged Yemen's warring parties to respect a ceasefire accord struck at peace talks in Sweden after deadly clashes in the port city of Hudaida.
The Saudi-led coalition admitted Saturday that "mistakes" had been made in an August air strike on Yemen that killed 51 people including 40 children, adding that those responsible must be "punished."
The raid which killed at least 40 children was, according to Saudi Arabia's UN representative, "legitimate" and targeted Houthis "responsible for recruiting and training young children," Saudi TV reports.
The US military is the only force known to operate armed drones over Yemen, a country ravaged by war since 2014.
Doctors say medicine prices have skyrocketed and hospitals are running out of supplies as well as money as the country struggles with diphtheria, cholera and malnutrition.
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