Hector Ivan Mejia, another spokesman for the security ministry, told the Reuters news agency that several of the bodies had been beheaded.
The victims of the violence, which began late on Friday, were part of a group of 57 transferred to the National Penitentiary from the San Pedro Sula prison after nine prisoners were killed there.
"At this moment, we have issued instructions across the country to ensure that the group that was transferred from the San Pedro facility to other locations are guaranteed their safety so this does not happen again," Jorge Rodas, minister for public security, said.
"We regret this very much. We are now looking to secure other prisoners who are in danger and keep them separate."
Ivan Mejia, a police spokesman, said the dead men belonged to an organisation known as Peseta.
"They are young men who used to belong to the Mara 18 or to the MS and they were going through a rehabilitation process," he said.
Maras are street gangs which are often involved in drugs and weapons trafficking.
The Central American country's 25 prisons are overflowing with around 12,000 inmates.