Thousands ran into the streets in panic, and millions lost electricity when the quake struck around lunchtime.
Mexico City Mayor Miguel Angel Mancera said 44 buildings were severely damaged or destroyed. Several major gas leaks and fires occurred.
Interior Secretary Miguel Angel Osorio Chong told local television that rescue teams were working painstakingly with picks and shovels.
“We have some buildings where we have reports that there could be people inside. They are doing it with lots of caution,” he said, adding that more rescue personnel would be needed.
Ambulances and fire engines confronted gridlock on Mexico City’s streets as millions of workers tried to go home.
The temblor occurred on the 32nd anniversary of a devastating quake that killed thousands in Mexico City in 1985. Many Mexicans had taken part in earthquake drills on Tuesday as is customary every September 19.
A powerful quake in southern Mexico on September 7 killed at least 98 people.
Among buildings that collapsed in the capital on Tuesday were apartment blocks, a school, a factory and a supermarket. The fashionable Roma district was hard hit, and a six-storey apartment building was among several collapses reported.
Hundreds of volunteers and rescue workers dug through the rubble with picks, shovels and their bare hands.
“My wife is there. I haven’t been able to communicate with her. She is not answering, and now they are telling us we have to turn off our cellphones because there is a gas leak,” said Juan Jesus Garcia, 33, choking back tears.
On Twitter, relatives posted pleas for news of family members, including eight-year-old Alexis Vargas Macias who was at school when the quake hit.
Earthquakes of magnitude 7 or above are regarded as major and are capable of causing widespread heavy damage.
The worst-hit area appeared to be Morelos State, just south of Mexico City, where at least 54 people died. The epicenter of Tuesday’s quake was located in the central state of Puebla, the U.S. Geological Survey said, and 41 deaths were reported there.
Power was cut to 3.8 million customers, national electricity company CFE said.
In the capital, at least one survivor was pulled from a collapsed building in the busy Condesa neighborhood, and another was rescued from a six-story apartment building nearby.
In Cuernavaca, a city in Morelos popular as a destination for weekend visitors from Mexico City, there were reports on local radio of people trapped beneath collapsed buildings.
Mexican TV and social media showed cars crushed by debris.
“We got out really fast, leaving everything as it was and just left,” said Rosaura Suarez, as she stood with a crowd in Mexico City.
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