At a news conference in Mexico City Tuesday, Murillo Karam said 99 suspects have been detained so far. Authorities have also obtained hundreds of testimonies, confessions and pieces of evidence.
"These and other elements we found during the investigation allowed us to carry out an analysis about the logical causes and, without a doubt, we can conclude that the students at the teachers' college were abducted, killed, burned and thrown into the San Juan River, in that order," Murillo Karam said.
As to why they were killed, Tomás Zerón de Lucio, the head of Mexico's Criminal Investigations Agency, said it was a case of mistaken identity. In other words, the criminal group accused of executing the students thought they belonged to a rival gang, also operating around the town of Iguala where the students were last seen.
"... we can conclude that the motivation was consistent (with the theory that) the students were identified by the criminals as members of an organized crime rival group that operated in the region. That was the reason why they were deprived of their freedom, initially, and then of their lives," Zerón de Lucio said.
Former Iguala Mayor Jose Luis Abarca has been charged in the case and is awaiting trial as the accused mastermind of the abduction and execution of the 43 students. Authorities say he wanted to prevent the students from disrupting an event by his wife the night they went missing.
The students were believed to have been captured by Iguala police and turned over to a gang. There is no indication that Abarca wanted them all dead, authorities said, but the gang mistook them for a rival group and executed them.
Abarca's wife, Maria de los Angeles Pineda, has also been charged.
'Just can't dwell here'
The case has caused an uproar in Mexico, with countless protests and demonstrations, which at times turned violent.
At a news conference Tuesday, the parents of the students refused to believe authorities, even suggesting the Mexican military might've been behind the disappearance of the young men. The students attending a rural teachers college were left-wing, anti-government activists, mostly in their late teens and early twenties.
Murillo Karam categorically denied the army had anything to do with the case, saying there weren't even enough soldiers in the area at the time of the disappearance to abduct and execute 43 students.
Part of the problem is that so far the remains of only one student have been positively identified and parents are asking what happened to the other 42.
But the head of the Criminal Investigations Agency says the remains were so badly burned that extracting DNA samples for identification is now impossible. The ashes were thrown into the nearby San Juan River.
"The dental remains found in what was the middle of the fire show that the temperature reached 1,600 degrees Celsius (2,912 degrees Fahrenheit), which dehydrated, decomposed, intervened and fused the remains. This makes it impossible to extract DNA samples, even with the most advanced technology," Zerón de Lucio said.
At a public event, Mexico's President said Tuesday it's time to turn the page.
"I'm convinced that we should not remain trapped in this instant, this moment in Mexico's history, of sorrow, of tragedy and pain. We just can't dwell here," Peña Nieto said.