Suspected gang members have confessed to killing more than 40 students missing for six weeks, Mexican Attorney General Jesus Murillo has said.
He said three alleged gang members claimed the students were handed over to them by police.
They said some were already asphyxiated and they shot the others dead, before setting fire to all the bodies.
A total of 43 students went missing after clashing with police on 26 September in the town of Iguala.
A spokesman for their families said they would not accept they were dead until it had been officially confirmed by Argentine forensic scientists working on the case.
Bags found near river
The suspects from the Guerreros Unidos drug gang were recently arrested in connection with the disappearances.
Relatives of the missing said they had been told that six bags of unidentified human remains had been found along a river near where the students vanished.
Mr Murillo warned that it would be difficult to identify the charred remains and that authorities would continue to consider the students as missing until DNA tests confirmed the identities.
Previous searches have uncovered mass graves in the area, but initial tests suggested they did not contain the remains of the students.
Mr Murillo showed videotaped confessions by the suspects who said they had loaded the students into dumper trucks and taken them to a landfill site in Cocula, a city near Iguala.
About 15 of the students were already dead when they arrived and the rest were shot, according to the suspects.
Mr Murillo said the bodies were then burned with petrol, tyres, firewood and plastic in an inferno that lasted for 14 hours.
"The fire lasted from midnight to 2pm the next day. The criminals could not handle the bodies (for three hours) due to the heat," he said.
He said that the suspects then crushed the remains, stuffed them into bags and tossed them in a river.
Mr Murillo showed videos of investigators combing through small pieces of burned remains that were found in black plastic bags.
The suspects said they were not sure how many students they had taken but one said there were more than 40, Mr Murillo added.
"The high level of degradation caused by the fire in the remains we found make it very difficult to extract the DNA that will allow an identification,'' he added.
At the scene: Will Grant, BBC News Mexico correspondent
In what was at times a very graphic press conference, Attorney General Jesus Murillo laid out his office's findings into the disappearance of the students.
When they were handed over to the gang, around 15 of the students had already died from asphyxiation, he said. The remaining students were shot dead near a rubbish dump.
At that point, members of the gang - according to their own testimony, video clips of which were shown by the attorney general - burnt the students' bodies in a pyre.
Human remains from the river are now to be identified by experts in Austria, but Mr Murillo said it wasn't clear how long the process would take.
However, relatives of the missing remained sceptical. The families have been highly critical of the investigation into the students' disappearance.
"As long as there are no results, our sons are alive," Felipe de la Cruz, the father of one of the disappeared, said in a statement.
"Today they're trying to close the case this way... a blatant way to further our torture by the federal government."
The case has shocked Mexico. Thousands have staged protests over what they say is collusion between officials and organised crime, along with government inaction.
President Enrique Pena Nieto has faced widespread criticism and on Friday he vowed to hunt down all those responsible for the "horrible crime".
The students from a teacher training college in Ayotzinapa, in Guerrero state, had travelled to nearby Iguala to protest against what they said were discriminatory hiring practices, and to collect funds for their college.
But they went missing after clashes with the police.
Six people were also killed after police opened fire and witnesses described seeing the students being bundled into police cars.
More than 70 people have been arrested in connection with the disappearances, including the Mayor of Iguala, Jose Luis Abarca, and his wife, Maria de los Angeles Pineda, who were detained in Mexico City on Tuesday.
Mexican officials accused Mr Abarca of ordering police to confront the students to prevent them from disrupting a public speech given by his wife.
Timeline: Iguala disappearance
26 Sept: Students from a teacher training college in Ayotzinapa travel to Iguala to protest and raise funds
Night of 26 Sept: Police stop the students, 6 people are shot dead, 43 students disappear
30 Sept: Iguala mayor Jose Luis Abarca asks for leave from his post, which is granted
4 Oct: Mass graves are found near Iguala containing 28 bodies
19 Oct: Federal police are deployed to Iguala and replace the municipal force
22 Oct: Mexico's prosecutor general says an arrest warrant has been issued for Mr Abarca, his wife and the town's police chief
23 Oct: Guerrero state governor Angel Aguirre resigns
29 Oct: President Enrique Pena Nieto meets the relatives of the missing students and promises a "renewed search plan"
4 Nov: Mr Abarca and his wife are arrested in Mexico City
7 Nov: Three gang members confess to killing students and burning their bodies, according to Mexico's attorney general