The bodies were found after police received an anonymous call, a spokesman of the Guerrero attorney general's office told Efe.
State police, federal police officers and army troops provided security for the crime scene investigators who located the graves and started the process of digging up the remains.
Investigators said the bodies' advanced state of decomposition indicates that the victims were murdered about a year ago, the AG's office spokesmen said.
The clandestine graves were found Saturday morning at a site just north of Zumpango known as Ojito de Agua. The 13 bodies recovered Saturday were taken to the coroner's office, which will try to identify the victims using genetic and other information.
Human remains were discovered in the same area more than a year ago. Eleven bodies were found buried Nov 9, 2012, near the clandestine graves found this weekend.
Los Rojos, a gang formerly affiliated with the Beltran Leyva drug cartel, operates mainly in Chilpancingo, the capital of Guerrero, and Zumpango.
The gang runs extortion rackets, stages kidnappings and steals cars in Chilpancingo, a city with a population of about 200,000.