The 43 students abducted by police in Mexico have been officially declared dead for the first time, despite the fact that remains of only one person have been identified.

Parents accuse the government of trying to close an investigation that has implicated security forces, the army and a mayor in a case that shocked the world.

Mexico’s Attorney General, Jesus Murillo Karam, told families of the missing students that their children had been rounded up by police and handed over to a drug gang, who murdered them and incinerated their bodies at a rubbish dump, mistaking them for rival cartel members.

“The evidence allows us to determine that the students were kidnapped, killed, burned and thrown in the river,” said Mr Murillo.

In emotional scenes at Tuesday night’s conference in Guerrero state, relatives rejected the theory which was first put forward two months ago, with some believing the students could still be alive.

“We don't believe anything of what they say,” said Carmen Cruz, mother of missing 19-year-old Jorge Cruz. “We are not going to allow this case to be closed.”

Mr Murillo said evidence of petrol, diesel and burnt rocks and steel from the inside of tyres at the scene proved the theory and that the fire was hot enough to burn all 43 bodies to ashes - a claim that has been disputed by Mexican scientists.

Protests in Mexico over 43 missing students Show all 13 1 /13 Protests in Mexico over 43 missing students Protests in Mexico over 43 missing students Mexican protests Demonstrators tear down the barricades in front of the main entrance of the Mexican National Palace at the Main Square (Zocalo) during a demonstration in Mexico City on November 8, 2014 Protests in Mexico over 43 missing students Mexican protests A group of students try to tear down the main entrance of the National Palace at the Main Square (Zocalo) during a demonstration in Mexico City on November 8, 2014, demanding justice Protests in Mexico over 43 missing students Mexican protests A demonstrator with her mouth taped shut and the number 43 painted on her face marches in protest of the disappearance of 43 students AP Protests in Mexico over 43 missing students Mexican protests Students protest at the disappearance of 43 students in the state of Guerrero, outside the general attorney's office in Mexico City AP Protests in Mexico over 43 missing students Mexican protests Demonstrators march in protest for the disappearance of 43 students in the state of Guerrero, in Mexico City AP Protests in Mexico over 43 missing students Mexican protests Big scale posters showing images of 43 missing students are displayed during a march in Mexico City, Mexico EPA Protests in Mexico over 43 missing students Mexican protests A police officer stands in front of protesters holding up a banner during a demonstration to demand justice for the 43 missing students from the Ayotzinapa teachers' training college AP Protests in Mexico over 43 missing students Mexican protests Thousands of people participate in a march in Mexico City, Mexico EPA Protests in Mexico over 43 missing students Mexican protests People walk near photographs of the missing student teachers from the Ayotzinapa Teacher Training College Raul Isidro Burgos, in Chilpancingo Reuters Protests in Mexico over 43 missing students mex-1.jpg Protestors, and family of 43 missing students from Guerrero State in Mexico protest in the Zocalo to demand answers from the government of the missing students on November 5, 2014 in Mexico City, Mexico Protests in Mexico over 43 missing students Mexican protests Students protest at the disappearance of 43 students in the state of Guerrero, outside the general attorney's office in Mexico City AP Protests in Mexico over 43 missing students Mexican protests A singer performs in front of photographs of the 43 missing students of the Ayotzinapa Teacher Training College Raul Isidro Burgos Reuters Protests in Mexico over 43 missing students Mexican protests Protesters demonstrate in the Zocalo and demand answers from the government about the 43 missing students from Guerrero State in Mexico Getty Images

Remains found in bags in a river had traces of the dump where the fire occurred but scientists who conducted forensic testing on the ashes at a specialist laboratory in Austria only identified one victim, Alexander Mora.

It was impossible to identify the other remains, they said.

Lawyer Vidulfo Rosales, who is representing the families of the students from a rural teaching college, presented a 10-point argument for the investigation to continue, including a lack of conclusive forensic results.

A woman holds a portrait of her missing son during a protest outside the heavily guarded Los Pinos Presidential palace (Getty Images)

A number of key suspects remain at large, who said, who could shed new light on the official version of events on the night of 26 September.

Mr Rosales said the families would be presenting a formal complaint to the Committee on Enforced Disappearances at the UN Office of the High Commissioner for Human Rights next week.

The Mexican government “will have to respond for these events,” he added.

The Attorney General’s conclusion was based in part on the testimony of a suspect arrested two weeks ago who told police he was called to “get rid” of the students.

Parents of the 43 students missing in Iguala, Guerrero, accompanied by thousands of supporters, march to commemorate the fourth month since their disappearance, in Mexico City on 26 January (EPA)

Felipe Rodriguez Salgado, otherwise known as “El Cepillo”, is member of the Guerreros Unidos gang who is alleged to have taken part in the kidnapping, murder and disappearance of the students.

But the families have cast suspicion on his testimony, as well as that from other criminals, pointing to incentives to lie for plea deals and cut sentences, as well as the history of torture within the Mexican police.

“A criminal's word cannot be worth more than ours,” Mrs Cruz said.

There have so far been 39 confessions, 386 declarations, 487 forensic tests, 16 raids and two reconstructions as part of the investigation, with 99 detained, including the former mayor of the city of Iguala, Jose Luis Abarca.

Earlier this month, a student from the group who escaped the massacre implicated the army in the disappearance but Mr Murillo denied that soldiers participated in the killings or allowed them in any way.

People walk near photographs of the missing student teachers from the Ayotzinapa Teacher Training College Raul Isidro Burgos, in Chilpancingo (Reuters)

The Mexican government had questioned, but not charged, 36 soldiers, and relatives have demanded access to army barracks in the area where they believe the students may have been taken.

Its latest explanation is unlikely to quell the controversy that has caused widespread protests in the last four months and forced a nationwide show of a crackdown on crime.

On Monday, relatives of the students led a huge march in Mexico City demanding government action and concrete proof of what had happened.

The motive for the alleged murders continues to raise questions, with the Attorney’s General claim the students were mistaken for rival gang members contradicts the testimony of suspects who said they knew they were students.

There is no known reason for the Guerreros Unidos targeting the group from the Raúl Isidro Burgos Rural Teachers' College of Ayotzinapa, which has a tradition of left-wing political activism.

A portrait of Guerrero governor Angel Aguirre Rivero is burnt at the Government palace in Chilpancingo

They travelled to Iguala and commandeered a number of buses as part of a protest but were intercepted by local police on the journey who allegedly shot at them before rounding them up and driving them away in police cars. They were never seen again.

“We know the who, the what, the when and the where. We don't know the why,” said analyst Alejandro Hope. “They have yet to tell a compelling story of why this happened. It doesn't matter how many people they detain - unless they answer that question, the whole thing will remain under a halo of mystery.”