The Hurricane Center said Katia could still bring 3 to 6 inches of additional rain to a region prone to deadly flooding.
Hurricane Katia is strengthening as it bears down on Mexico's Gulf coast.
The worst hit was the Zapotec indigenous city of Juchitán in Oaxaca.
"Not another one. God, please no", said one woman, falling to her knees to pray. "Every time a auto passes by, I feel like it's an quake".
Elsewhere, a Category 5 Hurricane Irma left a string of deaths and damage across the Caribbean, battering Cuba late Friday with winds of 160 miles per hour (257 kph) and bearing down on south Florida. "At first I laughed, but when the lights went out I didn't know what to do". It's hard. My sister-in-law's husband died. His house collapsed on top of him.
The Interior Department reported that 428 homes were destroyed and 1,700 were damaged in various cities and towns in Chiapas.
The governor said tens of thousands of ration packs, blankets and cleaning kits were arriving, along with 100 federal police reinforcements with rescue dogs to search for people in the wreckage.
Alejandro Murat told local television that 17 of the deaths were recorded in the southeastern town of Juchitan.
Mexico's capital escaped major damage, but the quake terrified sleeping residents, many of whom still remember the catastrophic 1985 natural disaster that killed thousands and devastated large parts of the city. The massive 8.1 quake killed at least 61 people, authorities said. "In many cases the walls have cracked or collapsed completely".
Ignacio Chavez said his son died in the quake.
Officials said the death toll there could rise.
The official added that the storm had left some 70,000 people without electricity and caused damage in 53 of the Gulf state's 212 municipalities, Reuters reports.
The quake, which struck shortly before midnight local time in the Pacific Ocean, about 60 miles off the coast of the state of Chiapas, leveled hospitals, churches and the city's main government buildings.
Thursday's quake was 756 kilometres from the city. To the east, Hurricane Jose, a Category 4 storm, was following behind, threatening further damage in Irma's wake.
Sirens wailed across Mexico City warning its estimated 20 million population of a rapidly approaching quake from the Pacific, the latest use of its effective early warning system.
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