Police, firefighters and ordinary Mexicans dug frantically through the rubble of collapsed schools, homes and apartment buildings early Wednesday, looking for survivors of Mexico's deadliest earthquake in decades as the number of confirmed fatalities stood at 217.

Adding poignancy and a touch of the surreal, Tuesday's magnitude-7.1 quake struck on the 32nd anniversary of a 1985 earthquake that killed thousands. 

One of the most desperate rescue efforts was at a primary and secondary school in southern Mexico City, where a wing of the three-story building collapsed into a massive pancake of concrete slabs. Journalists saw rescuers pull at least two small bodies from the rubble, covered in sheets.

Volunteer rescue worker Dr. Pedro Serrano managed to crawl into the crevices of the tottering pile of rubble that had been Escuela Enrique Rebsamen. He made it into a classroom, but found all of its occupants dead.

"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.

"We can hear small noises, but we don't know if they're coming from above or below, from the walls above (crumbling), or someone below calling for help."

A mix of neighbourhood volunteers, police and firefighters used trained dogs and their bare hands to search through the school's ruins. The crowd of anxious parents outside the gates shared reports that two families had received WhatsApp messages from girls trapped inside, but that could not be confirmed.

Rescuers brought in wooden beams to shore up the fallen concrete slabs so they wouldn't collapse further and crush whatever airspaces remained.

The federal Education Department reported late Tuesday that 25 bodies had been recovered from the school's wreckage, all but four of them children. It was not clear whether those deaths were included in the overall death toll of 217 reported by the federal civil defence agency. Pena Nieto had earlier reported 22 bodies found and said 30 children and eight adults were reported missing.

In a video message released late Tuesday, Pena Nieto urged people to be calm and said authorities were moving to provide help as 40 per cent of Mexico City and 60 per cent of nearby Morelos state were without power. But, he said, "the priority at this moment is to keep rescuing people who are still trapped and to give medical attention to the injured people."

People across central Mexico already had rallied to help their neighbours as dozens of buildings tumbled into mounds of broken concrete. Mexico City Mayor Miguel Angel Mancera said buildings fell at 44 sites in the capital alone as highrises across the city swayed and twisted and hundreds of thousands of panicked people ran into the streets.