President Enrique Pena Nieto described the 8.2 magnitude quake as "a major earthquake in scale and magnitude, the strongest in the past 100 years."
The southeastern Pacific coast states of Oaxaca and Chiapas appeared to have borne the brunt of the damage, with 25 people killed in Oaxaca alone, Mexico's agriculture secretary Jose Calzada said.
The worst destruction appeared to be in Juchitan, Oaxaca, where 17 people were confirmed dead, state governor Alejandro Murat said on local television.
"There are houses that collapsed with people inside," Luis Felipe Puente, director general of the emergency response agency, told TV news channel Milenio.
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A hotel also collapsed in Juchitan, the town hall partly caved in, and many homes were badly damaged.
Seven people were killed in Chiapas and three people, including at least two children, were killed in neighboring Tabasco state, authorities said.
In Tabasco, one child was crushed by a collapsing wall.
Another, an infant on a respirator, died after the quake triggered a power outage.
The quake epicenter was about 100 kilometers from the coastal town of Tonala, in far southern Chiapas state, and hit at 11:49 pm yesterday (0449 GMT), Mexico's seismologic service said.
The quake shook a large swath of the country and was felt as far north as Mexico City -- some 800 kilometers from the epicenter -- where people fled their homes after hearing sirens go off as buildings trembled and swayed.
Many of those fleeing were in their night clothes. Some clutched babies and pets as they stumbled onto the streets.
"Not another one. God, please no," said one woman, falling to her knees to pray.
Onelia Guerra, an anxious Oaxaca local who was in the capital, was taking a plane back to home to check on her family.
"My father and my 14-year-old son are alone there," she told AFP.
The quake injured four people and damaged homes in neighboring Guatemala, the country's state disaster authority head Sergio Cabanas told reporters.
The quake struck as Mexicans were also bracing for the impact of Hurricane Katia, which strengthened to a Category Two storm as it rumbled towards the state of Veracruz on the Gulf coast.
Mexico is vulnerable to hurricanes, given its location and its Pacific and Atlantic coastlines, and is hit by a least a dozen weather events a year.
Speaking from the National Disaster Prevention Center's headquarters, where he was supervising the emergency response, Pena Nieto said that 50 million people out of Mexico's population of 120 million people felt the quake.
Mexican officials ordered schools to remain closed today in 11 states, including Mexico City, so they could inspect for structural damage.
The quake struck at a depth of 69.7 kilometers, according to the USGS.
It was later lifted, but Mexico remained on alert for aftershocks.
Since the 1985 earthquake, Mexican authorities have instituted a stricter building code and developed an alert system using sensors placed on the coasts.
Mexico sits atop five tectonic plates, whose movement makes it one of the most seismically active countries in the world.
Pope Francis, at an open air mass on a visit to Colombia, said he was praying "for those who have lost their lives and their families" in the quake.
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