Results show former VP Lenin Moreno of the Socialist Party has 51.12% of the vote, with just 4% of districts still waiting to be counted.
However, challenger Guillermo Lasso had already begun celebrations after an exit poll predicted his victory.
Guillermo Lasso demanded a recount, and called on supporters to take to the streets.
He also alleged electoral fraud had been used to grant victory to his opponent.
In a series of tweets, Guillermo Lasso told the public to “peacefully defend your vote” and said he was “going to defend the will of the people”.
Final official results have yet to be announced.
If Lenin Moreno is declared the winner, he will continue a decade of left-wing leadership begun by President Rafael Correa in 2007.
He would also become one of a small number of disabled world leaders – he became paraplegic after being shot in the back during a robbery in 1998.
An apparent victory for Lenin Moreno was welcomed by WikiLeaks founder Julian Assange – as Guillermo Lasso had vowed to evict him from his asylum in the country’s London embassy if victorious.
Julian Assange tweeted that he “cordially invites” Guillermo Lasso to leave the country within 30 days – referencing the timeframe the candidate gave for Assange’s own eviction.
Guillermo Lasso, a former banker who wants to promote foreign investment, called for a recount after Lenin Moreno started to take a lead in the preliminary results.
Exit polls released on April 2 had suggested an extremely tight race.
A poll by Periles de Opinion had shown Lenin Moreno leading with 52.2%, while a poll by Cedatos showed Guillermo Lasso winning with 53.02%.
Incumbent President Rafael Correa, meanwhile, tweeted criticism of what he termed “violence” in several cities as early results emerged.
Local media reported that some of Guillermo Lasso’s supporters had gathered in the capital of Quito, as well as the city of Guayaquil. According to The El Comercio newspaper, the crowd removed barriers placed in the road, and bottles were thrown by some in Guayaquil.
When he was first elected in 2007, Rafael Correa was one of a group of left-wing leaders in power in Latin America.
However, in the decade since, conservative politicians have taken power in Argentina and Brazil. A victory for Guillermo Lasso would have continued that trend.
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