Nigerian President Muhammadu Buhari scored early gains on Monday as main opposition Peoples Democratic Party (PDP) accused the government of trying to manipulate results of last weekend's election.
The 76-year-old candidate of the ruling All Progressives Congress (APC) party won 57 percent of the vote in the southwestern state of Ekiti, the first to announce its results.
But PDP chairman Uche Secondus said the ruling APC was colluding with the electoral commission.
The APC was using "impeachments, manipulation, incarceration", state agencies and ministers to rig the outcome, he charged.
President Buhari, a former military ruler, is seeking a second term.
Analysts have been split about who will win -- the PDP candidate, former vice-president Atiku Abubakar, is mounting a strong challenge.
Mr Secondus told a news conference at Mr Abubakar's campaign headquarters that it would be "difficult for the entire country to accept this level of intimidation".
He called on INEC to "live up to its responsibility."
To win, a candidate needs a majority of votes and at least 25 percent of support in two-thirds of Nigeria's 36 states and the FCT.
A total of 72.7 million people were eligible to cast their ballot in Saturday's polls. Parliamentary elections were held at the same time.
The election -- the sixth in the 20 years since Nigeria returned to democracy after decades of military rule -- was held on Saturday, a week after a last-gasp postponement.
The Independent National Electoral Commission (INEC) blamed logistical difficulties, which were not entirely ironed out by this weekend, forcing voting to go into a second day.