Ukraine's interior ministry said at least 31 people had died in the fire with local media reporting that pro-Russian militants were believed to have been in the building at the time.
Most of those who were killed died from smoke inhalation, while others perished trying to escape by jumping out of windows.
News of the deaths came after a day of violent clashes between pro-Russian and pro-Ukrainian militants, with reports of renewed fighting in Slavyansk late today leading to the death of two more Ukrainian soldiers, meaning at least nine people had been killed in clashes in the flashpoint town throughout the day.
US Secretary of State John Kerry also this evening announced the postponement of a phone call with the Russian Foreign Minister Sergei Lavrov as tensions mounted.
While Obama was speaking, an emergency meeting of the UN Security Council took place at Russia's request, to complain about the Ukrainian army's assault on the flashpoint town of Slavyansk.
The Kremlin said the raid was "leading Ukraine towards catastrophe" and pronounced dead a peace deal struck in Geneva last month to ease the worst East-West confrontation since the Cold War.
Ukraine's interim president Oleksandr Turchynov said "many rebels" had been killed in the military's pre-dawn raid on the eastern town of Slavyansk and confirmed the loss of two servicemen after insurgents shot down two helicopter gunships.
Rebels later said three of their number and two citizens were killed in what they said was a "full-scale attack". They vowed to defend the town, which has become the epicentre of tensions in increasingly volatile eastern Ukraine.
The attack seemed to dash hopes of a quick release of seven European monitors being held in Slavyansk, with one senior rebel leader saying it would result in a "delay".
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