Residents were advised that tsunami waves could hit within three hours off the coasts of Mexico, Guatemala, Panama, El Salvador, Costa Rica, Nicaragua, Honduras and Ecuador.
An quake of a preliminary magnitude of 8.0 struck off the coast of Chiapas, Mexico, late on Thursday local time, the Pacific Tsunami Warning Center (PTWC) said, citing USGS data.
Part of a bridge on a highway being built to the site of Mexico City's planned new global airport collapsed due to the quake, local media reported.
Officials said the death toll there could rise. That includes 37 in Juchitan.
The furious shaking created a second national emergency for Mexican agencies already bracing for Hurricane Katia on the other side of the country.
State authorities in Oaxaca, Chiapas and Tabasco, the regions hardest hit by the quake, have updated known deceased, bringing the total to 61.
"The power of this natural disaster was devastating", Pena Nieto said, speaking from Juchitan de Zaragoa, a city in Oaxaca state where at least 36 people died. The storm has since dissipated.
The death toll from the massive quake that struck Mexico on Thursday night has risen to at least 90 after emergency services in the southern state of Oaxaca said late on Saturday there had been 71 confirmed fatalities in the state alone.
The state government says more than 1,000 homes were destroyed in Chiapas, and about 5,000 were damaged. As of Saturday, officials reported 36 people dead in that town. The quake was so string that it was felt in Mexico City which is 600 miles from the epicenter.
Yunes said 2,886 had been evacuated from their homes across the state. The State Secretariat of Education reported 792 schools damaged by breaks and extensive cracks.
Hurricane Katia has deteriorated into a soggy tropical depression that is dumping rain over the mountains of east-central Mexico.
It weakened as it made landfall on Friday night.
Hurricane Irma was downgraded to a Category 3 storm, but is still causing widespread damage in the Caribbean. Lots of damage. Lots of deaths.
At least 80 people have been hospitalized in the Isthmus region of Oaxaca with injuries sustained during the quake, which is being described as the strongest ever recorded in Mexico.
Scenes of mourning were repeated over and over again in Juchitan, where a third of the city's homes collapsed or were uninhabitable, President Enrique Pena Nieto said late Friday.
Katia was lashing the state of Veracruz, which borders the Gulf of Mexico, as well as parts of Hidalgo and Puebla.
Mexican authorities evacuated almost 10,000 coastal residents amid fears of a tsunami, but the Hawaii-based Pacific Tsunami Warning Center said later that the tsunami threat had passed.