The USGS says there have been more than thirty aftershocks, ranging from 4.2 to 5.7 in magnitude.
Puente said those three southern Pacific states near the epicenter were the most affected by the natural disaster.
At least 61 people have died in Mexico after the country was struck by its most powerful natural disaster in a century.
Chiapas Gov. Manuel Velasco told Foro TV that there have been reports of damage, including hospitals that have lost power and buildings with collapsed roofs, CNN reported. The government has reportedly ordered evacuations in some areas as a safety measure.
Tsunami waves hit the southern coast of Mexico after a magnitude 8.1 quake struck shortly before midnight local time. He also confirmed that majority had their power restored later on Friday. Authorities have advised people to look for structural damages to their homes and gas leaks.
The U.S. Geological Survey initially estimated the magnitude at 8.0 before revising it to 8.1 The Mexican Seismological Agency rated it at magnitude 8.4.
Chiapas, the area hardest-hit by the quake, is home to several popular tourist attractions.
"According to the preliminary data, five people have died [as the result of the earthquake], material damages have been sustained", the President said at the press conference. The quake also rocked one of the city's major landmarks, which is the Angel of Independence monument.
The country's President, Enrique Peña Nieto, described the quake as the strongest in a century.
The area is seismically active, and has experienced eight other earthquakes measuring between 7.0 and 7.5 over the past 100 years.