The quake struck at 18:58 local time on Saturday (23:58 GMT) near the northern coastal town of Muisne.
Widespread severe damage is reported, with a bridge destroyed as far south as Guayaquil about 300km (190 miles) away.
A state of emergency has been declared in six provinces and the National Guard has been mobilised.
The quake, the country`s largest in decades, also shook buildings in the capital, Quito.
President Rafael Correa is cutting short his trip to Italy to return home. He called for calm, saying on Twitter: "Our infinite love to the families of the dead."
Mr Glas said that at least 77 people had died and 588 had been injured, and that emergency services, police and the army were "in a state of maximum alert to protect the lives of citizens".
Gabriel Alcivar, mayor of the town of Pedernale, which is close to the epicentre, said: "We`re trying to do the most we can but there`s almost nothing we can do."
He said dozens of buildings had been flattened and looting had broken out.
"This wasn`t just a house that collapsed, it was an entire town," Mr Alcivar said.
Ecuador earthquake of 7.8 magnitude kills 77 people
17 April 2016
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A powerful 7.8-magnitude earthquake in Ecuador has killed at least 77 people and injured more than 500, Vice-President Jorge Glas says.
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