Rescuers swarmed over rubble with shovels and picks on Thursday in a frantic search for survivors two days after Mexico's deadliest earthquake in a generation, focusing on 10 collapsed buildings where people may still be alive.

Those trapped included five Taiwanese workers in a textile factory in downtown Mexico City. But an official said a missing schoolgirl whose fate captured the nation "did not exist," leading to an outpouring of anger over the mix-up.

The death toll was at least 273, officials said. Mexico City Mayor Miguel Angel Mancera said 50 people were not accounted for.

Working without pause since Tuesday afternoon's 7.1 magnitude quake, first responders and volunteers have saved 60 survivors, from central Mexico City to poor neighbourhoods far to the south.

Mexico Earthquake

Rescue workers rest during search operations in Mexico City on Wednesday. (Miguel Tovar/Associated Press)

Late on Wednesday night, an eight-year-old girl was rescued from a collapsed building in the Tlalpan neighbourhood, nearly 36 hours after the quake, local officials said.

'I'm really traumatized'

Luis Manuel Carrillo Nunez, 14, said he was in a yoga class at the Enrique Rebsamen private school on Tuesday when he heard people yell, "It's shaking!"

He ran to escape the building as it began collapsing. But some classmates never made it out.

"It's hard to know that you're not going to see again the friends that you loved. I'm really traumatized," he said.

The full scale of damage has not been calculated, with buildings across the city of 20 million people badly cracked. Citigroup's Mexican unit Citibanamex told clients it was lowering its 2017 growth forecast to 1.9 per cent from 2.0 per cent due to the earthquake.

Some families made dangerous trips back into damaged structures to pull out possessions, and trucks with mattresses, furniture and televisions rumbled through the streets.

Help not reaching everybody

Despite a massive effort by volunteers and the armed forces to gather and distribute food and basic medicines, help has not reached everybody.

Thousands of people were sleeping in their cars, rather than going to shelters or damaged homes, and in the badly damaged streets in the south of the city some people held up signs begging for food.

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A woman hands out food to people after the earthquake in Jojutla de Juarez on Thursday. (Edgard Garrido/Reuters)

While food, water, medicine, blankets and other basic items have been donated, some residents complained that emergency services were slow to arrive to poorer southern neighbourhoods of the city, and that wealthier districts appeared prioritized.

Disaster relief is sensitive for politicians in Mexico after the government's widely panned response to the 1985 quake caused upheaval, which some credited with weakening the one-party rule of the Institutional Revolutionary Party (PRI).        

Search for schoolgirl who wasn't there

After more than a day of wall-to-wall television coverage of the search for a girl in the rubble of the Enrique Rebsamen school, the navy changed its version of events and said all pupils were now accounted for.

Since Wednesday, rescue workers told leading broadcaster Televisa that a schoolgirl was trapped in the rubble, a version confirmed by the admiral in charge of the rescue effort at the school, who on Thursday said the information came from the International Red Cross.

Senior navy official Angel Enrique Sarmiento said he believed one adult was still alive under the rubble. Rescue work continued at the school.

The search for the girl, whom some local media outlets named "Frida Sofia," captured hearts in a nation desperate for good news. As it became clear that the trapped person was not a child, there was an outpouring of anger on social media directed at broadcaster Televisa and the navy for raising hopes.

Eleven other children were rescued from the same school, where students are aged roughly six to 15, the navy said, adding that 19 children and six adults there were killed.

The body of a woman was pulled out on Thursday morning.

'We were bouncing up and down'

Lourdes Huerta, 10, was on an upper floor of a part of the school that did not collapse and returned to the site Thursday with her mother as the rescue was underway.

Crews desperately try to rescue victim in collapsed Mexican school1:04

When the quake struck, "it was like we were bouncing up and down," Huerta said, nervously fingering a stuffed animal. "When I left the classroom the whole school was moving and we couldn't go downstairs, so we went back into the classroom and huddled up against the walls."

She said she was terrified when a wall collapsed, but said if they had tried the stairs "we would have ended up being thrown about."

In the middle of a nearby avenue Thursday evening, about 50 people attended a special mass, including aggrieved families and rescuers from the school site. Sobs broke out when the priest spoke the names of the dead, as cars passed by in both directions.

Mexico Earthquake

People attend an outdoor Catholic mass Thursday near the Enrique Rebsamen school that collapsed in Mexico City. (Rebecca Blackwell/Associated Press)

The ceremony ended with the release of white balloons that floated toward the heavens. "My brave princess," one of them read, "we will always love you."

Earlier in the day, rescuers removed dirt bucketful by bucketful and passed a scanner over the rubble every hour or so to search for heat signatures that could indicate trapped survivors. Shortly before dawn the pile shuddered ominously, prompting those working atop it to move away.

The shaky wreckage was reinforced with massive iron beams, each requiring a dozen or more men to carry and lift into place. Stretchers were brought to the edge of the building, and a large crane was also on site.

5 trapped in collapsed factory

The Taiwanese Ministry of Foreign Affairs confirmed five nationals were trapped in a collapsed clothing factory in the Obrera neighbourhood. Volunteers cutting through debris at the factory, which had been combed by rescue dogs, heard signs of life from a car.

Rescue worker Amaury Perez said, "We shouted, 'If you are inside the vehicle, please knock three times.' He knocked three times."

Crews from Panama, El Salvador, the United States and Israel joined the search, using dogs, cameras, motion detectors and heat-seeking equipment to detect victims who may still be alive. 

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Members of Israeli and Mexican rescue teams and volunteers search for survivors in the rubble of a collapsed building in Mexico City on Thursday. (Henry Romero/Reuters)

     

Armed soldiers guarded abandoned buildings at risk of collapse. Some 52 buildings collapsed in Mexico City alone and more in the surrounding states.

Questions over construction standards

The extensive damage to many buildings, some of them relatively new, raised questions over construction standards that were supposed to have improved after a 1985 quake.

The quake came on the anniversary of the 1985 earthquake that killed thousands and still resonates in Mexico. Annual Sept. 19 earthquake drills were being held a few hours before the nation got rocked once again.

Mexico was also recovering from another powerful quake less than two weeks ago that killed nearly 100 people in the south of the country.

With files from The Associated Press