Officials said almost 1.3 million votes would be recounted after allegations of fraud by the losing candidate - former banker Guillermo Lasso.
Mr Lasso has refused to accept anything less than a full recount.
His rival, the Socialist candidate, Lenin Moreno, won the second round with a slim majority of 51.15%.
He is set to replace his fellow socialist, President Rafael Correa, at the end of May.
The recount of the equivalent of 1.2 million votes, which would account for 12% of the total votes cast, will take place on Tuesday in public in the capital Quito.
The council has not disclosed what sort of ballots would be recounted.
The electoral authorities in Ecuador have ordered a partial recount of the votes cast in the presidential election earlier this month.