Commission chairman, Mahmood Yakubu, told a news briefing in the capital Abuja Sunday that collated results from a handful of Nigeria's 36 states would be announced from Sunday evening.
"I appeal to all political parties and media organizations to draw their figures only from the official results released by the Commission as the only body constitutionally responsible for releasing official election figures," Yakubu said.
A final tally for the country's presidential and parliamentary elections is expected within five days.
On Saturday evening, hundreds of voters were still in line to cast their ballots several hours after voting officially ended.
Some of them say they had been waiting in queue since 5 a.m., more than three hours before the polls opened.
Frustration was getting to many.
"I'll sleep here, and I'm ready to sleep until tomorrow. I'm not longer in a hurry. Anytime they're ready, we will be ready, too. I have mattress and my pillow; everything is here already," one voter told VOA.
Some Nigerians returned to the polls Sunday after technical and other problems prevented them from casting their votes Saturday.
"The whole process is an absolute mess," Preye Iti, 60, a civil servant, told Reuters. "I waited from 8:30 a.m. to 6:30 p.m. yesterday. Now I'm back here at 8:30 again."
The Independent National Electoral Commission briefed journalists Saturday afternoon and said the delay has been caused by setbacks in deployment of staff and election materials to those areas, as well as security threats.
It was not clear how many of Nigeria's 93 million registered voters were unable to cast a ballot on Saturday.
In most parts of the country of 200 million people, voting went smoothly. Despite scattered incidents of violence and intimidation, this was not on the scale of previous elections.
Saturday's election pit former Lagos governor Bola Tinubu, 70, of the ruling All Progressives Congress (APC) against an old rival, former vice president Atiku Abubakar, of the Peoples Democratic Party (PDP), 76.
But for the first time since the end of military rule in 1999, a third-party candidate, Peter Obi of the Labour Party, has challenged the APC and PDP dominance with a campaign message of change.
A total of 18 candidates contested for Nigeria's top position.
Spread over more than 176,000 polling units, voters also cast their ballot for Nigeria's two houses of parliament, the National Assembly and Senate.
Information in this report came from Reuters and Agence France-Presse. VOA’s Timothy Obiezu also contributed.