Most deaths have come in the state of Oaxaca.
The 8.1 magnitude earthquake is the most powerful to hit Mexico in a century, with the town of Juchitan on Mexico's narrowest point, hit particularly hard.
Oaxaca govenor Alejandro Murat says civillians have the government's support.
Also in Mexico, Hurricane Katia has made landfall near a beach resort in the state of Veracruz [ver-A-cruise] on the Mexican Gulf coast.
The category 1 storm landed with sustained gusts of 120 kilometres per hour, over half the wind speed of Hurricane Irma, and is not expected to do much damage.