The inmates were shot dead by snipers, writes the national guard on Telegram.
Before that, the inmates killed four guards at the prison. Three of them are reported to have died immediately and the fourth at the hospital. Three more guards are receiving hospital care for their injuries, announces the prison service.
In total, eight guards and four fellow prisoners were taken as hostages.
"Unfortunately, people have died as a result of the criminals' actions", writes Governor Andrej Bocharov on Telegram.
The incident is said to have occurred in Surovikino in Volgograd, southwestern Russia.
Russian independent Meduza has published recordings where the alleged rioters express support for the Islamic State and for those suspected of the terrorist attack on a concert hall in Moscow in March.
This is the second time in a few months that a similar incident has occurred in a Russian prison.
