Confusion and sporadic violence has blighted Nigeria's tensest presidential election since the end of army rule.
Opposition supporters are disputing results from a southern state even before they have been announced.
The opposition All Progressives Congress (APC) in Rivers state accused supporters of President Goodluck Jonathan of being behind killings of its campaigners, and denounced the vote there as "a sham and a charade".
The INEC election commission said the first results collated from 120,000 polling stations nationwide should be available this evening.
Turnout among the 56.7m registered voters appears to have been high.
The election pits Mr Jonathan against former military ruler Muhammadu Buhari for the favour of an electorate divided along a complex mix of ethnic, regional and in some cases religious lines in Africa's most populous nation.
Dismissal of the vote in Rivers, the centre of Africa's biggest oil industry, raises the prospect of a disputed national outcome and the risk of a repeat of the violence.
After the last election in 2011, 800 people were killed and 65,000 displaced in the mainly Muslim north.
The APC reported violence in Rivers and blamed it on "armed militias" backed by the ruling People's Democratic Party (PDP).
"Whatever trash will (be) announced as the result of today's election is not acceptable to us," it said.
Hundreds of sympathisers chanted "APC" outside the electoral commission office in the oil city of Port Harcourt, prompting police to fire warnings shots. One group stoned a car they thought carried ballots.
"There was no election in Rivers," APC polling agent Achinike William-Wobodo told Reuters, calling for a re-vote.
In a sign the opposition will challenge results elsewhere, the APC governor of the southern Imo state, Rochas Okorocha, denounced on television the conduct of the election in his region and accused the military of meddling in the result.
INEC chairman Attahiru Jega said he was concerned about the Port Harcourt complaints, which alleged that opposition agents were kicked out of vote-tallying meetings, and had launched an investigation.
Kano and Kaduna, the northern cities worst-hit by the 2011 post-election violence, were calm.
Mr Jonathan's PDP was no less scathing about the election,accusing the APC of using underaged voters.
Voting in yesterday's election was extended into today at a handful of polling stations after technical glitches hit voter ID machines, including ones scanning Mr Jonathan's fingerprints,meaning he had to wait 40 minutes to vote.
The technology was introduced to prevent the ballot box stuffing, multiple voting and other fraud that characterised past polls, but the PDP was openly against their introduction from the start.
Islamist Boko Haram militants killed over a dozen voters in the northeast and at least two people were shot dead in Port Harcourt, which has a history of political thuggery.
This is the first time since the end of military rule in 1999 that an opposition candidate has had a serious chance of winning, raising the stakes compared to previous years.
PDP officials did not respond to a request for comment and it was not possible to corroborate the claim independently.
Anybody who announced results before the commission would be breaking the law, he added.
Mr Buhari and Mr Jonathan appealed for calm and signed a "peace accord" on the eve of the vote, but many Nigerians still fear a repeat of the post-election violence that erupted in 2011, when Mr Jonathan defeated Mr Buhari.
