After results from 14 of the 36 states of Nigeria were announced, Bola Tinubu, the candidate of the country's ruling party, is in the lead.
Just over 44% of the total votes have gone to Mr. Tinubu. Atiku Abubakar, his main rival, has received close to 33 percent of the vote.
Peter Obi, a member of the Labour Party, has nearly 18 percent of the vote after surprising Mr. Tinubu in Lagos, the country's largest city.
On Monday, the parties of Mr. Abubakar and Mr. Obi left the location where the results are being declared.
The new electronic voting system, according to the Peoples Democratic Party (PDP) and the Labour Party, lacks transparency.
This was the first national election in which voters were verified using an electronic device.
The Independent National Electoral Commission (Inec) rejected the complaints made by the opposition parties.
The results announcement will continue, according to its chairman Mahmood Yakubu.
The All Progressives Congress (APC), which is in power, was charged with conspiring with Inec by the PDP representative at the election center in the nation's capital, Abuja. The Labour Party requested that the results be withheld or that the election be canceled and rescheduled.
According to the APC, those who are unhappy with the outcomes should file a lawsuit before getting in court, and the parties should first let the procedure play out.
For a candidate to be declared the winner, they must receive more than 50% of the votes cast nationally and 25% of the votes cast in each of the 25 states plus Abuja.
There will be a run-off between the top two candidates in the event that those thresholds are not met.
Since the military took over in 1999, the APC and PDP have dominated Nigeria.
Previously unknown Labour Party candidate Mr. Obi ran for office for the first time, vowing to upend the two-party system.
Many young people, who make up a third of registered voters, support him. There are 15 additional contenders.
According to the results so far released, Mr. Tinubu received the most votes across six states, followed by Mr. Abubakar with five and Mr. Obi with three.