Incumbent President Goodluck Jonathan is a native of the southern oil-rich Niger Delta region that's predominantly Christian and animist. His nearest rival is former Gen. Muhammadu Buhari, who comes from the mainly Muslim north, the BBC said.
Election officials said turnout among the more than 74 million registered voters was high Saturday, but results weren't due to be released until Monday.
A candidate must win at least 25 percent of the vote in two-thirds of the country's 36 states, or a run-off election would be called, the report said.
Africa's largest country has a history of election fraud, but Buhari told the BBC he had more faith in the Independent National Electoral Commission this time.
"Probably 60 percent of the election will be credible," he said.
Violence has also been a problem in previous elections. Two bomb blasts were reported in the northeastern city of Maiduguri and a woman was killed in the central city of Jos, but few other details were released.