Some buildings did not fall immediately, giving people time to escape, and some shattered but left air spaces where occupants survived.
Mayor Miguel Angel Mancera said there were no reports of significant new damage in the capital, and rescue efforts related to Tuesday's quake were continuing.
The United States Geological Survey reports of a 6.2 magnitude quake that hit Mexico's southern state of Oaxaca, Sputnik reported.
A hospitalized survivor spoke to CNN about his ordeal after being trapped in rubble for 17 hours.
But even while the city and county stand ready to help, several Mexican nationals and members of the business community also are aiding the relief effort.More news: Protesters rally against Iranian president at United Nations
"Since September 7 it has not stopped shaking", he said. This is around 530km south of Mexico City.
Those who saw the buildings collapse said the tragedy could have been much worse.
The Government of Mexico (GoM) continues to coordinate a robust national and worldwide response to the magnitude 7.1 quake that struck central Mexico on September 19, killing at least 305 people, injuring more than 2,600 people, and damaging more than 20,000 buildings, according to the latest GoM and global media reports.
Pereda said she didn't want to leave: "I was anxious about him".
The tremor was mild in Mexico City but thousands of residents, many wearing pyjamas, ran into the streets when seismic alarms sounded. The combined death toll from the two events is thought to be over 400.More news: 3.4 magnitude natural disaster possibly triggered by nuclear test hits North Korea
Pereda said she feels like people are getting accustomed to being on edge.
Dielen also said in the statement that they have been assured that, while the authorities' immediate priority will be dealing with the aftermath of the earthquakes, the 2017 World Archery Congress and Championships should continue as planned.
Senior officials said there could be 20,000 badly damaged homes in the states of Morelos and Puebla.
In Oaxaca, some highways and a bridge that had been damaged during the September 8 natural disaster collapsed, Mexico's federal police said.
So far there have been no reports of injuries, fatalities or damage, reports news outlet 24 Horas.More news: Korea near nuclear test site
Rescuers said the Israeli teams came with equipment enabling them to detect cell phone signals in the rubble.
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