He said security forces later regained control and slowly began discovering bodies in a kitchen, a cellblock and other areas. Three people were injured in addition to 28 dead, of which four were decapitated.
Thursday's riot at Las Cruces, which houses more than 2,000 prisoners, was one of the worst outbreaks of violence in Mexico's prison system in recent years.
"The incident was triggered by a permanent feud between rival groups within the prison", explained Roberto Alvarez, a state security spokesman.
After hearing news about the deadly riot, inmates' families rushed to the prison and pleaded for the police to give them information.
Acapulco was one of Mexico's most popular tourist destinations, but an explosion of violence was recorded as rival gangs are fighting to control illegal activities.
Some desperate relatives tore down a section of the prison's fence trying to get to their loved ones.
Acapulco is the biggest city in Guerrero, one of Mexico's most lawless states and a centre for opium poppy production.
What was the once-glamorous resort of Acapulco has turned into a city struggling with a high number of killings.
A USA embassy official could not provide details about the Homeland Security chief's activities on Thursday.
Early past 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.
In March 2017, 29 accused drug cartel members allegedly tunneled their way out of a prison in Tamaulipas state.
A report issued last month by Mexico's governmental rights agency said numerous country's prisons are unsafe, overcrowded and understaffed.
The National Human Rights Commission said it surveyed conditions at over 190 state, local and federal jails. All of the casualties, he said, were caused by improvised weapons that inmates fabricated.