The announcement came after Moreno's conservative challenger Guillermo Lasso refused to recognise the results of Sunday's election, demanding a recount.
The National Electoral Council (CNE) President, Juan Pablo Pozo, urged either of the two political parties to submit their claims by using the corresponding institutional channels. He also called his supporters to fill the streets to guard against fraud.
Hundreds of Lasso supporters gathered outside the National Electoral Council's headquarters in Quito for the third straight night of mostly peaceful protests that contrasted with the more unruly behaviour seen on election night, when supporters crashed through metal barricades in Quito and scuffled with riot police in several cities.
"We predict that they will deny our request, but in the denial of our requests is confirmation of the fraud", he said.
The Lasso campaign said it detected irregularities such as missing signatures, inverted results and incorrect tallies at 1,795 of the nearly-40,000 voting acts processed nationwide.
"By force they want to achieve what they can't at the ballot box", he said on Twitter.
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Despite resounding praise for the transparency of Sunday's vote from worldwide observation missions, right-wing former candidate and banker Lasso has contested the outcome of the vote on unsubstantiated claims of fraud, calling for a recount.
For weeks Ecuadoreans polarised by 10 years of Correa's iron-fisted rule had been bracing for a contested vote.
Yet in the final weeks of the race, Moreno inched ahead in polls amid an aggressive campaign led by Correa to cast Lasso as a wealthy, out-of-touch politician who profited from the country's 1999 banking crisis.
Wikileaks founder Julian Assange may have narrowly escaped eviction from Ecuador's embassy in London but he has some work to do building trust with his new host. Before the election, Lasso had said he would evict the Australian activist, who is wanted for extradition by Sweden, within 30 days of taking office.
The socialist president-elect's conservative rival, Guillermo Lasso, had vowed to kick Assange out of the embassy.
"I cordially invite Lasso to leave Ecuador within 30 days (with or without his tax haven millions)", he tweeted - a reference to allegations the ex-banker has money stashed in offshore accounts.