Loud, sustained bursts of gunfire could be heard from just outside the gates of the lockup in Ciudad Victoria, the capital of Tamaulipas state, as heavily armed security forces stood guard.
A state police officer who emerged from the prison with scratches on his face and did not give his name said the inmates were armed with automatic rifles. He spoke briefly to The Associated Press while being taken to an ambulance for treatment.
Police and soldiers were mobilized to try to restore order.
"The operation continues," Rodriguez said Tuesday night. Government photos from a helicopter overflight showed what appeared to be white smoke rising from one building.
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Authorities closed nearby roads, and surrounding areas were under an evacuation alert.
Relatives of prisoners said the violence apparently broke out due to a conflict between local inmates and others who were recently transferred from a prison in the border city of Nuevo Laredo.
Tamaulipas, a Gulf coast state bordering Texas, has seen high levels of violence in recent years as rival drug gangs and factions battle for control.