Digging through the night and into the morning, rescue workers and residents searched frantically for survivors of a powerful earthquake that turned high-rise buildings into piles of rubble and collapsed a school attended by hundreds of children.

In harrowing scenes that horrified Mexicans, rescuers pulled the bodies of dozens of children from the ruins of the elementary school.

The 7.1-magnitude quake, which struck early afternoon, killed more than 200 people across central Mexico - in the capital and five states - but there were fears that the toll could rise as additional victims were extracted from the debris.

Volunteers and rescue workers search for children trapped inside the Enrique Rebsamen school, collapsed by a 7.1 earthquake in southern Mexico City. Photo / AP
Volunteers and rescue workers search for children trapped inside the Enrique Rebsamen school, collapsed by a 7.1 earthquake in southern Mexico City. Photo / AP

For hours after the country was hit by its second earthquake in less than two weeks, Mexicans worked in the dark, often with their bare hands, to find trapped survivors. Power was out across 40 per cent of this city of 20 million, and rescue and medical services were stretched to their limits.

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Volunteers, medics and marines toiled side by side to clear away the chunks of concrete in the dusty air. Everywhere in the city, they formed lines to pass along containers filled with rubble and dump them into waiting trucks.

Cries of "silence" punctuated the work as people listened in hope for the sounds of survivors under the wreckage. At least 44 buildings collapsed or partly collapsed in Mexico City alone, according to Mayor Miguel Ángel Mancera.

The temblor struck 122km southeast of the earthquake-prone capital at 1.14pm, according to the US Geological Survey, and came on the 32nd anniversary of the infamous 1985 quake that killed thousands.

Mexico's civil protection agency put the death toll at 225.

Rodrigo Arelia, a student who escaped from the rubble of his Enrique Rebsamen school, stands outside the building that collapsed during an earthquake in Mexico City. Photo / AP
Rodrigo Arelia, a student who escaped from the rubble of his Enrique Rebsamen school, stands outside the building that collapsed during an earthquake in Mexico City. Photo / AP

Even as residents were trapped inside buildings across the city and in the surrounding towns, attention was riveted on a collapsed private elementary school in the southern part of the capital. Before dawn, soldiers and police sealed off the blocks around the three-story Colegio Enrique Rebsamen. All through Tuesday afternoon and night (local time), rescue workers pulled dead children from the rubble and searched for survivors.

"This was really, really, ugly. Really bad," said Jose Pineda, 65, a hardware store worker whose children used to attend the school. "Everything has fallen."

A block away, neighbours had strung up sheets up paper, taped between a tree and a cross-walk sign, with names of children who survived, suffered injuries, or died. There were 31 names on the two lists of dead. At least 59 names were on the list of those who went to various hospitals.

"There are around 600 children at the school," said Elena Villaseñor, 44, a neighbour who was managing the notices. "We don't know how many children are still inside. They were in classes. The school was full."

Overnight, a stream of parents, grandparents and other relatives visited the sign to check for the names of their family members on the lists.

Rescue workers search for people trapped inside a collapsed building in the Condesa neighbourhood of Mexico City. Photo / AP
Rescue workers search for people trapped inside a collapsed building in the Condesa neighbourhood of Mexico City. Photo / AP

"It is very hard to have to point them to these two lists," Villaseñor said, motioning to the blue and white sheets with the names of the dead children. "There aren't words."

Rescue worker Pedro Serrano described to the Associated Press how he tunnelled into the unstable rubble to a partially collapsed classroom of the school, only to find no one alive.

"We saw some chairs and wooden tables. The next thing we saw was a leg, and then we started to move rubble and we found a girl and two adults - a woman and a man," he said.

However, workers did manage to rescue dozens of children from the wrecked school, Mexican news media reported. The daily El Universal described how one schoolgirl - identified only as Fatima - sent her parents a plea for help on the WhatsApp messaging service from her cellphone.

"I'm fine, I am trapped with four other kids, help us, we're thirsty," read the message, which reached her mother, six hours after the school collapsed, the newspaper said. She was later saved.

Residents salvage personal items from a home destroyed in a 7.1 earthquake, in Jojutla, Morelos state, Mexico. Photo / AP
Residents salvage personal items from a home destroyed in a 7.1 earthquake, in Jojutla, Morelos state, Mexico. Photo / AP

As Mexico City residents pulled together in solidarity, Parque Mexico in the badly affected Condesa neighbourhood became a campsite for people without shelter overnight and a dropoff point for blankets, food and medicine.

President Enrique Peña Nieto urged calm in a video message, saying "the priority at this moment is to keep rescuing people who are still trapped and to give medical attention to the injured people." He said 40 per cent of the capital and 60 per cent of neighbouring Morelos state were without power.

The President had been traveling to the southern state of Oaxaca to inspect damage from an earlier earthquake when the latest one occurred, sending him back to the capital to convene a national emergency council.

Nearly two weeks ago, an even larger quake off the Pacific coast shook the south of the country, killing close to 100 people. Scientists said the same large-scale tectonic mechanism caused both events: The larger North American Plate is forcing the edge of the Cocos Plate to sink. This collision generated both quakes. But it was unlikely that the quake earlier this month caused the disaster.

Mourners carry a coffin during a wake for 11 family members who were killed inside the Santiago Apostol church during the 7.1 earthquake in the town of Atzala in Puebla state, Mexico. Photo / AP
Mourners carry a coffin during a wake for 11 family members who were killed inside the Santiago Apostol church during the 7.1 earthquake in the town of Atzala in Puebla state, Mexico. Photo / AP

Mexico is particularly vulnerable to earthquakes: The country is in a region where a number of tectonic plates butt up against one another, with huge amounts of energy waiting to be unleashed.

Mexico City is partially built on old lake sediment, which is much softer than rock. The seismic waves can be amplified traveling through the sediment, according to Don Blakeman, a geophysicist with the USGS, making the damage worse than in areas on more-solid ground. He said aftershocks were possible, too. The rupture was approximately 50km and as a rule, the shallower an earthquake is, the higher the chance for aftershocks.

"Fifty kilometers is pretty shallow, so I would expect aftershocks," Blakeman said.

The USGS's model for estimating earthquake damage predicts 100 to 1,000 fatalities and economic losses of between US$100 million and US$1 billion for a temblor of this scale and proximity to population centers.

The quake shook Mexico City so hard that the murky, stagnant waters of the city's ancient Xochimilco canals turned into churning pools of waves. Videos posted to social media showed tourists in flat-bottomed tour boats struggling to stay in their seats and hold on to their beers.

Video appears to capture building exploding after magnitude 7.1 earthquake strikes Mexico City. Twitter / @mcantu06

In the central neighbourhood of Del Valle, a frantic scene played out as hundreds of people gathered to search for trapped residents. At least two multi story apartment buildings fell, and residents said dozens of people could have been inside.

At the Gabriel Mancera hospital in Mexico City, more than a dozen beds had been set up on the patio outside as a triage centre. Leticia Gonzalez, a 45-year-old maid in a nearby apartment building, said she tried to race out of the building but concrete crashed down as she fled. Her right leg was wrapped in a bandage as she grimaced in pain outside the hospital.

"We were all running like crazy," she said. "This was the worst earthquake I've ever seen."

Marisela Avila Gomez, 58, was in her apartment in the capital's central Narvarte neighbourhood when the shaking began, toppling her furniture and shattering the windows. A piece of glass sliced deep into her right leg.

"My whole house is full of blood," she said.

In a Twitter message after receiving news of the quake, President Donald Trump wrote: "God bless the people of Mexico City. We are with you and will be there for you."

In the capital's southern neighbourhood of Coyoacan, the walls of colonial-era buildings cracked and sagged in the quake, with some collapsing into rubble. Residents hugged and cried in the streets. At the Barricas Don Tiburcio shop, shelves bearing food crashed down and wine bottles shattered on the floors.

"This is the worst one I have ever felt," shopkeeper Beatriz Aguilar Bustamante said. "I don't know if I will have a house when I go home."