Remains could be 43 missing Mexican students Mexico's attorney general provides new details on the missing students He says police kidnapped them at the mayor's orders They were handed over to a gang, the attorney general says (CNN) -- The 43 Mexican students who disappeared in southern Mexico in September were abducted by police on order of a local mayor, and are believed to have been turned over to a gang that killed them and burned their bodies before throwing some remains in a river, the nation's attorney general said Friday. This is the conclusion that investigators have reached, Attorney General Jesus Murillo Karam said, though he cautioned that it cannot be known with certainty until DNA tests confirm the identities. This will be a challenge, he said, as the badly burned fragments make it difficult to extract DNA. "I have to identify, to do everything in my power, to identify, to know if these were the students," Murillo said. Parents of the college students reacted immediately, some saying the evidence is inconclusive and insisting that their children are alive. We are not going to believe anything until the experts tell us: You know what? It is them," Mario Cesar Gonzalez, the father of one of the students, told CNN en Español. Another parent, Isrrael Galindo, said the government is getting ahead of itself in an attempt to get protests over the disappearance of the students to stop and the public to stop demanding answers. "The government is trying to resolve things its way so that to rid itself of this great problem it is facing," Galindo, who lives in California but whose wife and children are in Mexico, told CNN en Español. My son is alive. My son is alive," he repeated. The parents have been highly critical of President Enrique Peña Nieto for his administration's handling of the investigation. A cell phone video from a closed-door meeting with the President, released on YouTube, shows family members accusing Peña Nieto of being out of touch with who the students are. One family member on the recording suggests the President should resign if he can't deliver answers. Describing the federal investigation as one of the most complex in recent times, Murillo outlined what he said befell the students from a rural teacher's college in Ayotzinapa, Guerrero state. Police linked to disappearance The victims were men mostly in their 20s studying to become teachers at a college in rural Ayotzinapa. On September 26, they traveled on buses and vans to nearby Iguala for a protest about lack of funding for their school. Three men arrested in connection with the disappearance of the students admitted to having killed a large number of people believed to be the students, Murillo said. Murillo said police officers handed the victims to the three men, who he said belong to the Guerreros Unidos gang. Authorities have arrested Iguala Mayor Jose Luis Abarca, called the "probable mastermind" in the mass abduction, and his wife, Maria de los Angeles Pineda. They were captured while hiding out in Mexico City earlier this week. The school the missing students belong to has a history that dates back more than 80 years and is known as a bastion of the Mexican left. Its students are known for their activism. Officials have said that when the mayor and his wife learned the students' protest would disrupt one of his events, the mayor ordered then-Iguala police Chief Felipe Flores Velasquez to stop the demonstration. The former police chief remains a fugitive. Slain Mexican student's friends, family demand justice Shortly after Murillo announced the latest in the investigation, President Peña Nieto said the findings "outrage and offend all of Mexican society." "With firm determination, the government will continue the efforts for a full accounting of the incident," Peña Nieto said. The capture of those who ordered it isn't enough; we will arrest everyone who participated in these abominable crimes. So far, 74 people have been arrested in connection with the disappearance of the students, the government said. Mexican governor steps aside after student kidnappings Officials: Men burned at dump Murillo on Friday repeated the claim that the order to abduct the students came from the mayor. The police confronted the students twice on their journey, killing three in one confrontation, and forcibly taking all of them to a police station the second time, the attorney general said. The students were then moved to a location where they were handed over to members of the Guerreros Unidos gang, he said. The gang members transported the students in various trucks to a garbage dump, Murillo said. Some were dead already, and those who were alive were questioned by gang members about their alleged involvement with other gangs, Murillo said. There is no evidence to show that the students were involved with gangs, he said. The attorney general identified the three gang members who confessed as Patricio Reyes Landa, Jhonatan Osorio Gomez and Agustin Garcia Reyes. The suspects told police they don't remember exactly how many people they killed, but they were told by their leaders that there were more than 40, Murillo said. The abducted men were then burned at the dump in a fire that was kept alive for at least 14 hours by adding diesel fuel, tires and debris, the attorney general said. The next day, the gang members were ordered to further break up the remains and place them in black garbage bags that were tossed into the San Juan River, Murillo said. Scuba divers searched the river and found pieces of the bags and remains. One bag was found intact, with human remains inside, the attorney general said. "I know the huge pain this information gives the families, a pain that we all share in solidarity," Murillo said. The protests spread to the capital, where tens of thousands marched this week demanding that the missing students be found alive. The governor of Guerrero state -- criticized for not acting quickly enough after the abductions -- has taken a leave of absence. CNN's Rafael Romo contributed to this report.