The quake came less than two weeks after at least 90 people were killed by an 8.1 magnitude tremor in the country's southern region.
September 19 - 20, 1985: Two earthquakes in western Mexico, one magnitude 8.0, kill at least 9,500 people in Mexico City and parts of central and western Mexico, heavily damaging parts of the capital.
Officials say at least 119 people are dead from the 7.1 magnitude natural disaster.
It came less than two weeks after a massive 8.1-magnitude quake hit the country on September 7 and killed almost 100.
The state of Morelos, just south of Mexico City, was also hard hit with 55 killed, Puente said.
The natural disaster took place on the anniversary of a devastating quake that killed thousands in Mexico City in 1985.
A man walks out of the door frame of a building that collapsed after an quake, in the Condesa neighborhood of Mexico City.
Emergency workers, aided by volunteers, are working through the night to search the rubble of collapsed buildings for trapped people.
Mr Peña Nieto was on a flight to Oaxaca, one of the hardest hit areas by the earlier quake, but said on Twitter that he was immediately returning to Mexico City.
"People are really scared right now", dentist Claudia Meneses who was in her clinic in Mexico City's Lindavista neighbourhood said of the confusion.
In addition, the federal interior minister, Miguel Angel Osorio Chong, said authorities had reports of people possibly still being trapped in collapsed buildings.
Screams can be heard as people quickly rush away from the building to safety as part of the block crumbles to the floor, causing a huge smoke cloud to rise into the air.
Rescuers have been searching for survivors, through the night, after Tuesday's powerful quake shook the capital, as well as surrounding states, killing multiple people and leaving many trapped under collapsed buildings.
The US Geological Survey (USGS) said the magnitude 7.1 quake was centered near the Puebla state town of Raboso, about 76 miles southeast of Mexico City.