Nigerian President Muhammadu Buhari scored early gains on Monday in his bid for re-election after dozens died in weekend violence and monitors voiced concern about polling-day problems.
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.
Buhari also won in neighbouring Osun state but he was run close by main challenger Atiku Abubakar, of the Peoples Democratic Party (PDP), winning by just over 10,000 votes.
A total of 72.7 million people with voter identity cards 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.
The Situation Room umbrella group of over 70 civil society organisations observing the vote, called for an inquiry into what it said was INEC's "poor management" of the process.
It highlighted lapses in logistics, technology and security and said INEC had "not managed the election efficiently and significant shortcomings have been recorded".
"The election has been a step back from the 2015 General Election and actions should be taken to identify what has gone wrong and what can be corrected," it added.
The head of the African Union observer mission, Ethiopia's former prime minister Hailemariam Desalegn, also said they were concerned "by the pattern of consistent postponement".
Elections were delayed by six weeks in 2015 on security grounds linked to the military counter-insurgency against Boko Haram Islamists in the country's remote northeast.
In 2011, voting was stopped even after it had started, again because of problems delivering ballot papers and other materials.
Hailemariam said the latest postponement had "implications for citizens' participation and turnout".
The National Democratic Institute and International Republican Institute said: "Last-minute election postponements should not become the norm in Nigeria."
It was "highly probably" voter turn-out had been affected, it said, adding: "Most significantly, the delay also undermined public confidence in INEC."
The election took place against a backdrop of fears about security across the country, as well as claims from both parties that the other was looking to rig the result.
Neither produced evidence but INEC chairman Mahmood Yakubu on Sunday said there were reports of ballot-snatching, vote-buying and violence.
One election volunteer was killed by a stray bullet in the southern state of Rivers, where some INEC staff and even police were held hostage before being released unharmed.
Other election staff were attacked in the southern state of Akwa Ibom and Kogi in the north central region.
The Situation Room, which had some 8,000 monitors on the ground, said "at least 39 Nigerians" were killed in election-related violence on Saturday and Sunday.
Worst-affected was Rivers, where 16 people were killed. Six other people lost their lives in the neighbouring states of Bayelsa and Delta, in the oil-rich Niger delta region.
Previously, analysts SBM Intelligence said 233 people were killed in 67 incidents of election-related violence from last October to Friday -- an average of two people per day.
The Situation Room highlighted reports that just over a quarter of the nearly 120,000 polling units were under-policed, and said there were "shortfalls and gaps" in security elsewhere.
At least six states saw disruption in polling. In the Okoto area of the country's biggest city, Lagos, voters were chased away and ballot boxes were destroyed.
In Osun state, ballot papers and boxes were destroyed at the local INEC office.
There were also reports of some "partisan" security officials, "compromised" INEC staff and incidents involving the military, including blocking some voters.
Police said separately that 128 people had been arrested across the country for electoral offences, including murder, vote-buying and ballot box snatching.