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. 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.

(CNN)