Despite a promise by the Independent National Electoral Commission (INEC) that it had overcome logistical difficulties that forced the postponement of last weekend's vote, some polling stations still opened hours late.
President Muhammadu Buhari was among the country's first voters and told reporters he is ready to congratulate himself.
According to a report by Sahara Reporters, residents of Maiduguri, the Borno State capital, are now in panic as series of explosions have rocked the city all within ten minutes.
The PDP, whose presidential contender is Atiku Abubakar, on the other hand said Inec had delayed the election to create "the space to flawless their rigging plans".
"There are some areas that need some attention especially on the delay in the time of commencement of voting".
Fears of a major Boko Haram attack have been growing in the run-up to elections, which the militants have previously vowed to disrupt. "I was expecting to see a huge turnout", he said, speaking on condition of anonymity because he was not authorized to speak to the press.
Candidates need to win the most votes and at least 25 percent support in two-thirds of Nigeria's 36 states and the Federal Capital Territory of Abuja.
Shortly before polls opened, one soldier was killed and 20 others injured as Boko Haram fighters tried to infiltrate the northeastern city of Maiduguri but were repelled.
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After last week's delay, many Nigerians were angered by the last-minute change and said they wouldn't vote.
The statement said the attack was repulsed and there were no casualties, adding that the situation is now calm in Geidam, allowing people to vote.
Buhari brushed aside reporters' questions about whether he would accept a loss to top challenger Atiku Abubakar, a billionaire former vice president. The president, first in line to vote in his northern hometown of Daura, jokingly checked the name on his wife's ballot.
The ailing Buhari has been criticized for not delivering enough on his promises to tackle insecurity, the economy and corruption. The 72-year-old businessman-turned-politician has been implicated in a number of corruption scandals over the years.
There was no official comment from the military but Borno police commissioner Damian Chukwu denied any attack.
Gunfire also was heard in Port Harcourt in Nigeria's restive south, where the military presence was heavier than in past elections.
Security is also a major concern; in the northeast, the Boko Haram insurgency continues, and in central Nigeria, herder-farmer conflicts over land and grazing rights have cost hundreds of lives.
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