The prison carnage was particularly embarrassing to Mexico as it came the same day US Department of Homeland Security (DHS) Secretary John Kelly was visiting Guerrero, which lies in the southwest of the country.
Guerrero state security official Roberto Alvarez told reporters that the fight broke out between rival gangs in the maximum security wing of the prison.
Authorities discovered bodies throughout the wing, including inside and just outside the kitchen, as well as the area for conjugal visits, he said.
A law enforcement official, speaking on condition of anonymity, told Reuters that four of them had been decapitated.
Kelly, one of the main links between the Mexican government and the Trump administration on migration and security cooperation, arrived in Mexico on Wednesday and has held meetings with top officials including President Enrique Pena Nieto.
Two Mexican officials said Kelly would be able to observe Mexico's efforts to eradicate poppies during his visit and two other officials said he had gone to Guerrero on Thursday.
The killings in Acapulco are the latest example of an upsurge in violent crime that has turned 2017 into one of the bloodiest years in the country's modern history.
Acapulco, one of Mexico's most famous beach resorts, was once a playground for Hollywood stars. However, in recent years it has been roiled by vicious gang warfare, and is now ranked one of the most murderous cities in the world.
Early last year, 49 people died in a battle between members of the feared Zetas drug cartel and rivals at a prison in the northern industrial city of Monterrey.
(Additional reporting by Lizbeth Diaz, Gabriel Stargardter and Dave Graham; Editing by Lisa Shumaker and Sandra Maler)
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