The 8.1-magnitude quake, which struck off the coast of Chiapas on Thursday, was the strongest the Latin American country had seen in a century.
The 1985 quake was by the coast, about 322 kilometres from Mexico City. That's where 37 of the 65 people killed by the quake lived.
The light damage so far is good news to national disaster officials who are already coping with the aftermath of a magnitude 8.1 quake that killed more than 60 people in southern Mexico. The city was shaken for between four to six minutes.
Classes were suspended in a dozen states, including Mexico City, to proceed with a structural review of schools.
Pope Francis said he was prayingfor those killed and bereaved by the quake. "Every time a vehicle passes by, I feel like it's an natural disaster".
Two more people are reported dead in Tabasco.
State authorities in Oaxaca, Chiapas and Tabasco, the regions hardest hit by the quake, have updated known deceased, bringing the total to 61.
Officials said the death toll there could rise.
In Juchitan "there are collapsed houses with people inside", Luis Felipe, the federal civil protection coordinator, told Televisa TV.
Reports indicate a hospital and the town hall are among the collapsed structures. The other, an infant on a respirator, died after the quake triggered a power outage. Projections based on population figures anticipate between 1000 and 10000 deaths. And it's likely to strike land just about a day after the country was hit by a major, magnitude 8.1 quake. Even the iconic Angel of Independence Monument swayed as the quake's waves rolled through the city's soft soil.
Economic losses from infrastructure damage is likely to be in the billions, it was reported. Nieto said one aftershock of 7.2 magnitude also occurred. Some were newly homeless, while others feared further aftershocks could topple their cracked adobe dwellings.
State spokesman Alfonso Martinez spoke by phone as he walked through the streets on Friday and said entire buildings had crumbled onto the sidewalks, reduced to scraps of bricks, adobes and wooden roof beams.
Smaller tsunami waves were observed on the coast or measured by ocean gauges elsewhere.