The Red Cross said it is seeking access to the prison in order to help with evacuating and treating the wounded.
Ukraine and Russia have accused each other of attacking the camp.
Unverified Russian video footage of the aftermath shows a tangle of wrecked bunk beds and badly charred bodies.
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Exactly what happened at the prison camp in Olenivka, which is controlled by the Russian-backed separatist Donetsk People's Republic, remains unclear.
Ukraine says the site was targeted by Russia in an effort to destroy evidence of torture and killing. President Volodymyr Zelensky described the incident as a "deliberate Russian war crime."
For its part, Russia said the camp was hit by Ukrainian precision rockets.
Those detained at the prison are said to have included members of the Azov battalion, who were captured defending the southern city of Mariupol in May and whom Russia has sought to depict as neo-Nazis and war criminals.
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