Recent opinion surveys have predicted the socialist Correa would win nearly 50 per cent of the vote, well ahead of his seven challengers. Such a win would allow Correa to meet Ecuador's constitutional standards to avoid a second-round election.
That an incumbent president is seeking re-election has made the current poll historic.
He would need to capture either a majority of the vote or a plurality of more than 40 per cent with a margin of at least 10 percentage points over the second-place candidate.
Polls indicate Correa's closest challenger, former president Lucio Gutierrez, would garner no higher than 14 per cent of the vote.
Mariana Sanchez, Al Jazeera's correspondent in the capital Quito, said: "Correa has remained popular amongst most Ecuadoreans throughout his presidency because he has invested millions of dollars to build roads and schools.
"He has even provided aid to poor single mothers with an $11 monthly bonus in cash," she said.
However, Sanchez said that Correa had lost some citizens' trust due to rising unemployment, and for failing to pay foreign debt that deterred foreign investment.
Since winning the presidency in November 2006, Correa has won three national votes, including a constitutional referendum.
The new constitution is the 20th since Ecuador was founded in 1830.
Preliminary official results for the presidential vote were expected to be issued late on Sunday. Results for the assembly and municipal votes would take longer since about 6000 seats were at stake.