MEXICO CITY - The 43 Mexican students who disappeared four months ago were murdered on the orders of a drug cartel who mistook them for members of a rival gang, the government said on Tuesday, finally confirming the deaths of the trainee teachers.

Their disappearance on the night of Sept. 26 in the southwestern city of Iguala led to massive street protests in Mexico and international condemnation of its security situation, embarrassing President Enrique Pena Nieto and plunging his administration into its biggest crisis.

Until now, the government had said only that the students were almost certainly murdered after clashing in Iguala that night with corrupt police officers, who handed them over to members of local drug gang Guerreros Unidos.

"There's no doubt that the students lost their lives, their freedom and were then incinerated and thrown into the Rio San Juan," Attorney General Jesus Murillo told a news conference, referring to a river by the town of Cocula, near Iguala.

Murillo has said the gang members suspected of killing the students had been so thorough in the destruction of their remains that it was difficult to identify them. The remains of only one of the missing students has been identified so far.

The mayor of Iguala and his wife were subsequently arrested as two chief suspects. The case has become notorious as an illustration of the nexus between organized crime and politics widely believed to exist across much of Mexico.

The attorney general's office said Felipe Rodriguez, an arrested member of Guerreros Unidos, had confessed to being given the order by one of his bosses to execute the 43 youths, who studied at a nearby leftist teacher training college.

"The students were identified by the criminals as members of the rival gang in the region," said Tomas Zeron, head of the criminal investigation agency at the attorney general's office.

Parents of the students accused the government of trying to close the case before it had been properly solved.

"We don't have enough evidence to accept this," said one of parents, Epifanio Alvarez.

The government said the gangsters believed the students had been infiltrated by a gang known as Los Rojos.

The attorney general dismissed that accusation against the students and said the investigation was continuing.

Murillo, who is seeking to have Rodriguez sentenced to up to 140 years in prison, also rejected media reports that the army was involved in the disappearances.