Guerrero State Prosecutor Inaky Blanco said the grave site was on the outskirts of Iguala, a town about 120 miles (200 kilometers) south of Mexico City. He did not say how many bodies were in the graves and declined to speculate on whether the remains could be the missing students.
"It would be irresponsible" to jump to conclusions before tests to identify the bodies, Blanco said.
Guerrero state Gov. Angel Aguirre said the victims had been "savagely slaughtered."
About 100 soldiers, marines and federal and state police cordoned off the area and kept journalists away from the burial pits, which were found on a hillside in rugged territory of Iguala's poor Pueblo Viejo district.
Juan Lopez Villanueva, an official with the federal government's National Human Rights Commission, said a total of six pits had been discovered but did not specify how many bodies were found. He also did not comment on whether the remains could be the students.
Blanco said eight more people had been arrested, adding to the 22 Iguala city police officers detained after a confrontation with student protesters late Sept. 27 set off a series of violent incidents in which six people were shot to death and the 43 young people were reported missing.
The prosecutor has said state investigators had obtained videos showing that local police arrested an undetermined number of students after the clash and took them away.
Blanco said some of the eight newly arrested people were members of an organized crime gang, adding that some of them had given key clues leading to the discovery of the mass grave.
The governor said earlier in the week that the investigation into the students' disappearance was looking at possible involvement of organized crime, which he charged has infiltrated the town government.
Vidulfo Rosales, a lawyer for a local human rights group who is assisting the families of the missing students, said before the burial site was found that relatives believed police turned the youths over to a drug gang.
"The suspicion, the hypothesis, is that they are being held by organized crime gangs that operated in collusion with the police," Rosales said.
State prosecutors have said the first bloodshed occurred last weekend when city police shot at buses that had been hijacked by protesting students from a teachers college. Three youths were killed and 25 people had wounds.
A few hours later, unidentified masked men fired shots at two taxis and a bus carrying a soccer team on the main highway, killing two people on the bus and one in a taxi.
Violence is frequent in Guerrero, a southern state where poverty feeds social unrest and drug gangs clash over territory.
The Aytozinapa Normal school attended by the missing students, like many other schools in Mexico's "rural teachers college" system, is known for militant and radical protests that often involve hijacking buses and delivery trucks.
In December 2011, two students from Aytozinapa died in a clash with police on the highway that leads to the Pacific coast resort of Acapulco. Students had allegedly hijacked buses and blocked the road to press demands for more funding and assured jobs after graduation. Two state police officers were charged in the shootings.
During that confrontation, students apparently set fire to pumps at a gas station on the highway when federal and state police moved in to quell the protest, and a gas station employee later died of burns suffered in the attack.
Published: 2014-10-05 11:25:04