“Why, why, why, damnable government?” beseeched Inés Abraján. “Why? Because you have the power!”

The plea from the aunt of Adán Abraham de la Cruz came as she headed a march of distraught and angry relatives of the 43 student teachers who “disappeared” and were probably massacred seven weeks ago, after they had been attacked by police in the southern Mexican city of Iguala.

The demonstration, part of a growing and passionate response to the killings that is gathering force across Mexico, passed through the streets of Tixtla, a town two hours’ drive from Iguala, where the students attended the Ayotzinapa college for rural teachers. “But we are not going to give up the struggle. We are not going to get tired,” Abraján told the marchers.

The pent-up fury of the parents reflected the intensity of the violent protests that marked a dramatic week in Mexico, which has deepened the political crisis facing President Enrique Peña Nieto as he returns from a week-long trip to China and Australia, seen by many as a sign of disdain for the suffering and anger at home.

“The government’s response has been shamefully poor, marked by carelessness for the lives of ordinary people, and only really concerned with damage control and trying to ensure this does not affect the flow of investment,” said Edgardo Buscaglia, a leading expert in international organised crime and political corruption around the world. “In situations like this, you end up with a social explosion and political instability, but the government doesn’t seem to see this.”

The week began with serious clashes between demonstrators and riot police in the resort city of Acapulco. A subsequent peaceful blockade of the airport left the building daubed with graffiti demanding Peña Nieto’s resignation.

On Tuesday, protesters set fire to the local headquarters of the president’s Party of Institutional Revolution in Chilpancingo, the state capital of Guerrero, where Iguala and Ayotzinapa are located. In the city of Xalapa, in the state of Veracruz, students put out the torch for the Central American Games by drenching a parade of athletes with water. After nightfall in Mexico City, thousands stood outside their homes and in public places, holding candles.

On Wednesday, fires raged and smoke billowed from the central offices of the Guerrero state government. In Amsterdam, chants of “Justice!” rang out from Mexican fans at the 43rd minute of a friendly football match with Holland.

Radical teachers in the state of Michoacán put 22 municipal halls under siege on Thursday, while students blocked roads in Chiapas and protesters in Oaxaca commandeered the contents of several vans distributing junk food, promising to send them to Ayotzinapa. Roadblocks, bus hijackings and assaults on public buildings continued in different parts of Mexico on Friday, while Peña Nieto found the disappeared students’ case pursued him to Australia where the Mexican community organised demonstrations in Brisbane, Canberra, Sydney and Melbourne.

The most significant thing the president said during his trip was on an outward stopover in Alaska, when he condemned an arson attack on the door of the ceremonial presidential palace in Mexico City. “Mexican society says no to violence,” he said, referring to the burning door. “We say yes to justice, order, harmony, tranquillity, and we say yes to the application of justice.”

The president made no mention of the fact that, immediately before the door was set on fire, the streets of the capital were filled with thousands of peaceful demonstrators. Many had carried banners proclaiming “ya me cansé”, which means “I’m tired” or “I’ve had enough”. The phrase was used by the attorney general, Jesús Murillo Karam, to cut short questions at the end of a press conference two days earlier, in which he had revealed the government’s new claim that the students were probably massacred in a rubbish tip not far from Iguala, hours after they had been arrested by municipal police and handed over to a local drug gang called Guerreros Unidos on 26 September.

Murillo said forensic examinations had corroborated gang members’ confessions that they piled the bodies of about 40 young people on to a huge funeral pyre that burned for about 15 hours, leaving only ashes and a few bone fragments to be collected in plastic bags and dumped in a nearby river. The fragments were sent to a specialist lab in Austria last week to see if identification was still possible.

Many parents, clinging to the hope that their children were still alive, said they doubted that such a fire could really cremate so many people. Some said it was raining on the night of the terror. They drew the saddest kind of comfort from last week’s news that DNA tests have ruled out that any of the students were among the 38 bodies recovered earlier from nine mass graves in the outskirts of Iguala. “They are hidden somewhere,” Clemente Rodríguez, father of Christian, told Associated Press. “I hope they’re going to let them go any day now.”

Even those convinced by the rubbish tip narrative point out how long it took the authorities to find something that must have been so blatant. Then there are the questions left unanswered, such as why they were killed, and how the government could claim that this was not a crime by the state. “A crime of state is much more serious,” Murillo had said at the now infamous press conference. “The state is not Iguala.”

The government’s efforts to contain the fallout to local politics dodges the protesters’ demand to know how the federal authorities did nothing about the collusion of the city’s municipal authorities with Guerreros Unidos. They had known for over a year that mayor José Luis Abarca, whom they now accuse of ordering the attack on the students, had been accused in 2013 of shooting a kidnapped activist in the face. There were longstanding reports of checkpoints into the city set up by the municipal police and the gang. On the night itself, the army remained in its barracks, just a few minutes from where the students were being attacked and disappeared over a period of hours.

“There is simply no way the army did not know what was going on,” said political commentator Raymundo Riva Palacio, who specialises in security issues. “What we don’t know is whether they didn’t go to help the population because of collusion or omission.” Riva Palacio insisted that the combination of generalised public anger, uniting the poverty-stricken rural families of the students with middle-class city dwellers, is providing the small but resilient guerrilla groups that have long roamed the mountains of Guerrero with a golden opportunity to try to deepen the contradictions in an effort to provoke an insurrection. There are also, he said, rumblings of discontent among the business elite.

“The incapacity of the government is so serious that, if things don’t change, the only thing they are going to end up doing is repressing the protest movement,” he said.

Some, including security expert Buscaglia, hope that the protest movement could develop into a peaceful force, with clear proposals for cleaning up the “corrupt political-business mafia” that will gather such momentum that politicians will have to comply. “I don’t see this happening yet,” he said, but added that he didn’t see the social protest movement fading away. “The government may be successful making Iguala disappear behind a lot of smoke and mirrors, but there are 22,000 disappeared people in Mexico, and every new mass grave that is found will be a trigger for more social pressure.”