Mexican Attorney General Jesus Murillo Karam has confirmed that forensic experts have identified the remains of one of 43 missing students.
Mr Murillo Karam said that tests matched a piece of bone retrieved from a rubbish dump in Guerrero state to the DNA of missing student Alexander Mora.
Relatives of Mr Mora had vowed to carry on fighting for justice.
The students' disappearance in September has led to protests across Mexico against corruption and violence.
Mr Murillo Karam told journalists in Mexico City that the students were handed over by corrupt officials to a criminal gang called Guerreros Unidos (United Warriors), after taking part in a protest in the town if Iguala on 26 September. .
They were taken to a waste disposal site near the town of Cocula and killed.
The criminals burned their bodies before scattering their ashes in a river, Mr Murillo Karam said.
Eighty people in total have been detained in connection with the trainee teachers' disappearance, including gang members, corrupt officials and local police.
The news that Alexander Mora's remains had been identified first emerged on Saturday, when relatives posted a message on Facebook.
During a demonstration in Mexico City on Saturday, parents of students spoke about the identification.
"If [the government] thinks that, because one of our boys' DNA was identified, we will sit and cry, we want to tell them that they're wrong," Felipe de la Cruz, father of a missing student, told the crowd.
"We will keep fighting until we find the other 42."
The unrest has seen President Enrique Pena Nieto's popularity rating drop to its lowest point since he took office two years ago.
In response, he has submitted a package of reforms to Congress that include replacing all 1,800 municipal police forces with state-level units.
Iguala Mayor Jose Luis Abarca and his wife, Maria de los Angeles Pineda were arrested at the beginning of November in Mexico City.
Mexican officials accused Mr Abarca of ordering police to confront the students to prevent them from disrupting a public speech given by his wife.