A relative of one of the 43 missing students listens during a news conference in Mexico city on Tuesday. Photo: AFP

Authorities in Mexico can now say with "legal certainty" that 43 students who went missing in September were killed by hit men working for a drug gang, the justice minister said on  ­Tuesday.

But parents of the students in a case that convulsed the nation and countries abroad insisted the case not be closed.

The disappearance of the men - all aspiring teachers attending a training college in the southern state of Guerrero - led to nationwide protests and a crisis for the government of President Enrique Pena Nieto.

Officials said the students vanished after gang-linked police attacked their buses in the city of Iguala, allegedly under orders from the mayor and his wife in a night of terror that left six other people dead.

The police then delivered the young men to members of the Guerreros Unidos drug gang, who told investigators they took them in two trucks to a landfill, killed them, burned their bodies and dumped them in a river.

The detained mayor of Iguala, Jose Luis Abarca, accused of giving the order to attack the students, is allegedly one of the heads of Guerreros Unidos.

The investigation "gives us the legal certainty that the student teachers were killed in the circumstances that have been described," Justice Minister Jesus Murillo Karam told a news conference.

Witness and expert testimony "have allowed us to ... come to the conclusion beyond a doubt that the students were abducted and killed, before being incinerated and thrown into the San Juan river, in that order," he said.

"It is the historic truth," said Murillo Karam. He played a video with testimony from ­detainees and footage from the investigation.

Until now, authorities had still officially considered the students to be missing.

Relatives of the victims, who marched on Monday with several thousand people in Mexico City to mark the four-month mark since their ­disappearance, have refused to accept the official explanation of events.

For now, only one of the students has been positively identified from charred remains, which leaves little hope of finding the 42 others.

"We the parents repudiate the way in which today the attorney general has sought to close the investigation," said Felipe de la Cruz, a spokesman for the relatives.

"We are not going to allow them to conclude or close the investigation," he added, surrounded by activists and parents. The latter still believe that the students are alive and are in the custody of security forces.