President Goodluck Jonathan and his ruling Peoples Democratic Party (PDP) were marginally ahead of his main challenger, as the first general election results came in on Monday.
Buhari and the APC won five states while Jonathan secured three states plus the Federal Capital Territory of Abuja, with nine results in. More results are expected from 1900 GMT.
The winning presidential candidate needs not just the most votes but at least 25 percent support in two-thirds of Nigeria‘s 36 states and the Federal Capital Territory to avoid a run-off.
The latter measure is designed to ensure a geographical spread of support across the country, with Nigeria divided along religious and ethnic lines.