Doctors Without Borders, a Paris-based relief agency also known as MSF, said the children were killed Saturday in coalition raids on a school in Haydan, a town in rebel-held Saada province.
The coalition of Arab states has been battling the Huthi rebels since 2015 after the insurgents seized Sanaa before expanding to other parts of the country.
Ten days ago it acknowledged "shortcomings" in two out of eight cases it has investigated of strikes on civilian targets in Yemen that the UN has condemned.
Coalition spokesman General Ahmed Assiri said the strikes hit a Huthi training camp, killing militia fighters including a leader identified as Yehya Munassar Abu Rabua.
"The site that was bombed... is a major training camp for militia," he told AFP. "Why would children be at a training camp?"
Yemen's government had confirmed to the coalition that "there is no school in this area", he said.
Assiri said MSF's toll "confirms the Huthis' practice of recruiting and subjecting children to terror".
"They... use them as scouts, guards, messengers and fighters," he said, noting previous reports from Human Rights Watch on the rebels' use of underage recruits.
"When jets target training camps, they cannot distinguish between ages," Assiri said.
- 'Recruitment of children' -
MSF spokeswoman Malak Shaher said those killed in the strikes on "a Koranic school" were all under 15.
She called on "all parties to take the measures necessary to protect civilians".
But Assiri criticised the organisation for overlooking the issue of child soldiers.
"We would have hoped MSF would take measures to stop the recruitment of children to fight in wars instead of crying over them in the media," he said.
The United Nation's children agency, UNICEF, also reported the attack.
It warned that "with the intensification in violence across the country in the past week, the number of children killed and injured by air strikes, street fighting and landmines has grown sharply".
The rebels posted pictures and videos on Facebook of dead children wrapped in blankets.
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Assiri sent AFP pictures of Huthi children carrying rifles and rocket-propelled grenade launchers.
Huthi spokesman Mohammed Abdulsalam said warplanes "targeted" children at the Jomaa bin Fadhel school, in what he called a "heinous crime".
The Arab coalition launched air strikes against the rebels on March 26, 2015.
After a three-month pause, it resumed raids on Tuesday, less than 72 hours after UN envoy Ismail Ould Cheikh Ahmed announced the collapse of peace talks.
Raids struck a food factory in the rebel-controlled capital, killing 14 people, medics said.
The factory is near a military equipment maintenance centre targeted by the coalition.
- UN concern -
The UN had voiced concern about the increased fighting over the past week, warning that more than 80 percent of Yemenis need aid.
"UNICEF calls on all parties to the conflict in Yemen to respect and abide by their obligations under international law," it said, including "to only target combatants and limit harm to civilians and civilian infrastructure".
Saudi Arabia reacted angrily to a decision in June to blacklist the coalition after a UN report found the alliance responsible for 60 percent of the 785 deaths of children in Yemen last year.
UN chief Ban Ki-moon had accused Saudi Arabia of threatening to cut off funding to UN aid programmes over the blacklist, a charge denied by Riyadh.
A 14-member investigative team formed by the coalition has probed claims of attacks on a residential area, hospitals, markets, a wedding and World Food Programme aid trucks.
It found the coalition guilty of "mistakenly" hitting a residential compound and an MSF-run hospital, but accused the rebels of having used the hospital -- also in Haydan -- as a hideout.
The UN says more than 6,400 people, mostly civilians, have been killed in Yemen since last March.
The coalition, meanwhile, said Saudi air defences Saturday intercepted a Scud missile fired from Yemen.
And the Saudi civil defence said six foreign workers at a water-bottling plant in Najran -- three Indians, two Bangladeshis and a Nepali -- were wounded when a factory was hit in a rebel bombardment from across the border.
Around 100 Saudi soldiers and civilians have been killed inside the kingdom's borders since last March.
The coalition has also been backing government forces fighting Sunni jihadists who have exploited the conflict to gain ground in southern Yemen.
On Sunday, government forces entered the southern city of Zinjibar as they launched an offensive to recapture the wider province of Abyan from the jihadists.