Vice President Jorge Glas said the death toll will likely rise further in what he called the "worst seismic movement we have faced in decades."
The quake, which struck at 2358 GMT last night about 170 km northwest of Quito, lasted about a minute and was felt across Ecuador, northern Peru and southern Colombia.
"Oh, my God, it was the biggest and strongest earthquake I have felt in my whole life. It lasted a long time, and I was feeling dizzy," said Maria Torres, 60, in the capital Quito, which was rocked by the late Saturday quake.
Glas said early today that the number of confirmed deaths has reached 77, and that more than 588 people were injured.
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"We know that there are citizens trapped under rubble that need to be rescued," he said in a special TV and radio broadcast.
Officials declared a state of emergency in the six worst-hit provinces.
Police, the military and the emergency services "are in a state of maximum alert to protect the lives of citizens," Glas said.
President Rafael Correa, on a visit to the Vatican, wrote on Twitter that he was immediately returning to Ecuador.
Ecuador's Geophysical Office reported "considerable" structural damage "in the area near the epicenter as well as points as far away as Guayaquil."
The US Geological Survey (USGS) said the 7.8-magnitude shallow quake struck off the northwest shore of Ecuador, just 27 kilometers from the town of Muisne. The vice president gave a slightly lower measurement of magnitude 7.6.
At least 55 smaller aftershocks rattled the country after the main quake, Glas said.
The Hawaii-based Pacific Tsunami Warning Center initially issued a warning for the nearby Pacific coastline but later said that the threat had largely passed.