'This egregious provocation was carried out to intimidate Ukrainian servicemen,' the defence ministry said.
Pushilin, the Donetsk leader, claimed Kyiv forces struck the jail because Ukrainian prisoners of war had begun to testify.
After a weeks-long siege and resistance at the Azovstal steel plant, the last stronghold of Mariupol, around 2,500 Ukrainian fighters surrendered in May.
Meanwhile, the General Staff of the Ukrainian Armed Forces said in a statement: 'The armed forces of the Russian Federation carried out targeted artillery shelling of a correctional institution in the settlement of Olenivka, Donetsk oblast, where Ukrainian prisoners were also held.
'In this way, the Russian occupiers pursued their criminal goals - to accuse Ukraine of committing 'war crimes', as well as to hide the torture of prisoners and executions...'
Mykhailo Podolyak, an adviser to Volodymyr Zelensky, said the Russian allegations were 'a classic, cynical and elaborate false flag operation' intended to discredit Ukrainian authorities.
Ukrainian authorities in the Donetsk region also said today that Russia has pressed on with the shelling of civilian targets in Ukrainian-held areas.
'The fighting in the region has been intensifying by the day, and civilians must evacuate while it's still possible,' said Donetsk Governor Pavlo Kyrylenko.
'The Russian army doesn't worry about civilian casualties. They are pummelling cities and villages in the region.'