Morelos Gov. Graco Ramirez earlier reported on Twitter that at least 42 people had died in his state south of Mexico City.
At least 11 others died in Puebla state, according to Francisco Sanchez, spokesman for the state’s Interior Department.
Gov. Alfredo del Mazo said at least nine had died in the State of Mexico, which also borders the capital.
Local officials in Mexico City reported at least four dead in the Benito Juarez borough alone.
Rescuers rushed to the sites of damaged or collapsed buildings in the capital, and reporters saw onlookers cheer as a woman was pulled from the rubble.
Rescuers immediately called for silence so that they could listen for others who might be trapped.
Mariana Morales, a 26-year-old nutritionist, 26, was one many who spontaneously participated in rescue efforts.
She wore a paper face mask and her hands were still dusty from having joined a rescue brigade to clear rubble from a building that fell in a cloud of dust before her eyes, about 15 minutes after the quake.
Morales said she was in a taxi when the quake struck, and she out and sat on a sidewalk to try to recover from the scare. Then, just a few yards away, the three-story building collapsed.
A dust-covered Carlos Mendoza, 30, said that he and other volunteers had been able to pull two people alive from the ruins of a collapsed apartment building three hours of effort.
“We saw this and came to help,” he said. “It’s ugly, very ugly.”
Alma Gonzalez was in her fourth floor apartment in the Roma neighborhood when the quake collapsed the ground floor of her building, leaving her no way out — until neighbors set up a ladder on their roof and helped her slide out a side window.
Gala Dluzhynska was taking a class with 11 other women on the second floor of a building on the trendy Alvaro Obregon street when the quake struck and window and ceiling panels fell as the building began to tear apart.
She said she fell in the stairs and people began to walk over her, before someone finally pulled her up.
“There were no stairs anymore. There were rocks,” she said.
They reached the bottom only to find it barred. A security guard finally came and unlocked it.
The quake caused buildings to sway sickeningly in Mexico City and sent people throughout the city fleeing from homes and offices, and many people remained in the streets for hours, fearful of returning to the structures.
Alarms blared and traffic stopped around the Angel of Independence monument on the iconic Reforma Avenue.
Electricity and cellphone service was interrupted in many areas and traffic was snarled as signal lights went dark.
The U.S. Geological Survey said the magnitude 7.1 hit at 1:14 p.m. (2:15 p.m. EDT) and it was centered near the Puebla state town of Raboso, about 76 miles (123 kilometers) southeast of Mexico City.
Puebla Gov. Tony Gali tweeted that there had been damaged buildings in the city of Cholula including collapsed church steeples.
Earlier in the day workplaces across the city held readiness drills on the anniversary of the 1985 quake, a magnitude 8.0 shake, which killed thousands of people and devastated large parts of Mexico City.
In that tragedy, too, ordinary citizens played a crucial role in rescue efforts that overwhelmed officials.
Market stall vendor Edith Lopez, 25, said she was in a taxi a few blocks away when the quake struck. She said she saw glass bursting out of the windows of some buildings. She was anxiously trying to locate her children, whom she had left in the care of her disabled mother.
Local media broadcast video of whitecap waves churning the city’s normally placid canals of Xochimilco as boats bobbed up and down.
Mexico City’s international airport suspended operations and was checking facilities for any damage.
Much of Mexico City is built on former lakebed, and the soil can amplify the effects of earthquakes centered hundreds of miles away.
The new quake appears to be unrelated to the magnitude 8.1 temblor that hit Sept. 7 off Mexico’s southern coast and which also was felt strongly in the capital.
U.S. Geological Survey seismologist Paul Earle noted that the epicenters of the two quakes are 400 miles (650 kilometers) apart and most aftershocks are within 100 kilometers.
There have been 19 earthquakes of magnitude 6.5 or larger within 250 kilometers of Tuesday’s quake in the past century, Earle said.
Earth usually has about 15 to 20 earthquakes this size or larger each year, Earle said.
Initial calculations show that more than 30 million people would have felt moderate shaking from Tuesday’s quake. The US Geological Survey predicts “significant casualty and damage are likely and the disaster is potentially widespread.”