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, reports Report citing BBC News.
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.
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.