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Attorney General Jesus Murillo told reporters that one of the students had been identified by experts in Austria from a bone fragment in a bag of ash and bits of burned tire found in a river where drug gang members said they tossed the students remains.
"This scientific proof confirms that the remains found at the scene coincide with the evidence of the investigation," Murillo said. "We will continue with the probe until all the guilty have been arrested."
One month ago, Murillo said that drug gang members had confessed to murdering the students and burning their bodies in a pyre of tires at an isolated dump.
But parents of the missing students have refused to accept the government's version and at a demonstration in Mexico City on Saturday night they said they would continue to demand more answers even after they had heard word of the DNA test results.
The apparent massacre has spurred widespread and sometimes violent protests throughout Mexico. Federal authorities waited 10 days after the students disappearance to intervene in the case, insisting it was a local matter.
Murillo said that 80 people have been detained in the probe, including the mayor of Iguala and his wife who are accused of ordering the police to get rid of the students from a radical left-wing college after they staged a demonstration in his town. Murillo promised more arrests, including 16 fugitive policemen.
During the search for the students in the state of Guerrero, dozens more bodies were discovered in mass graves. More than 100,000 people have been killed in Mexico in gang-related violence since 2007.
"There is a lot of rage, but it is not just this case," said political science student Jimena Rodriguez at the Saturday night march. "There are so many missing, and they do not have the least interest in really investigating."
(Reporting by Michael O'Boyle; Editing by Chris Reese)