Ban demanded once again that the UN Security Council refer Syria to the International Criminal Court so that the tribunal based in The Hague can open up investigations of possible war crimes.
"Those responsible for yesterday's seemingly calculated attack against civilians in the camp in Idlib, which could constitute a war crime, must be held accountable," said Ban's spokesman.
Women and children were reported to be among 28 civilians killed in the raids near the Turkish border, which also wounded 50.
UN spokesman Stephane Dujarric said it was "difficult to believe" that the air strikes were "a mistake", adding that there needs to be further investigation to determine who is responsible.
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The United Nations is working with its partners on the ground to collect information about the attack, said the spokesman, adding that countries that "have military assets should also take a look" at what happened.
Both Syria and Russia denied that the camp had been hit by an air strike and suggested that rebels could have shelled the site.
Ban has said that the starvation sieges and hospital attacks during Syria's five-year conflict are war crimes and that the ICC should put those responsible on trial.
Syria's conflict erupted in 2011 after anti-government protests were put down. Fighting quickly escalated into a multi-faceted war that has killed more than 270,000 people and forced millions from their homes.