The bodies, some of which are badly mutilated, are set to be fully identified within a month, according to statements from the Rio Grande do Norte state government on Twitter.
A day earlier, local media had said that 10 people were dead after fighting between the Comando de la Capital gang and its rival the Sindicato del Crimen broke out in the Alcacuz prison in the north-eastern city.
On Sunday, military police used helicopters and stun grenades to storm the facility, where they then discovered more dead bodies as a result of the fighting.
Brazilian media showed pictures of special forces lining up naked inmates in a row, after bringing the situation under control.
In the southern state of Parana, two inmates were also shot dead Sunday by military police as they attempted to flee a prison. Thirty people had escaped the facility after gang members blew up the prison wall from the outside.
Brazil has the world's fourth-largest prison population, which has led to overcrowding problems. More than 622,000 prisoners are held in cells that are only meant to house 371,884 people, according to official data.
At least 100 people have been killed in fighting inside Brazilian prisons since the beginning of this year.
