Nigeria's Independent National Electoral Commission (INEC) has declared results for 12 states so far, including the economic hub of Lagos, where incumbent governor Babajide Sanwo-Olu of the ruling party was reelected.
But observers say Saturday's elections were characterized by widespread violence, voter suppression and intimidation.
Local media reported that 21 people were killed and scores injured across the country.
In Imo state, police rescued 17 INEC staffers abducted by gunmen on the morning of the elections as they were heading to their polling units.
Rights group Amnesty International condemned the violence.
"There were pockets of violence and prevention of people to make their choices in the ballot, disrupting electoral processes and campaign of calumny, and the employment of thugs. We strongly condemn such human rights violations," said Aminu Hayatu, Amnesty International's conflict researcher.
Amnesty International said social media was used to incite tribal hatred and ethnic slurs and urged social media companies like Twitter, Meta and WhatsApp to improve their screening-out of hateful content.
There were also issues of staff delays and technical difficulties during Saturday's polls.
But Nigeria's information minister, Lai Mohammed, who voted in his hometown in south-west Kwara state, said the election was one of the most credible in Nigeria's recent history.
Idayat Hassan, director at the Center for Democracy and Development, disagrees.
"The likelihoods of postelection violence are high but how widespread is what we do not know," Hassan said. "Considering this is a projection, the response of the state is what we should actually be looking out for. How will the Nigerian state be able to timely nip any form of insecurity in the bud with the minimum use of force?"
Kano state authorities have imposed a dusk-to-dawn curfew in anticipation of unrest as more results are announced.
Amnesty International wants authorities to identify and punish promoters of election violence.
"Such are violations against the international human rights law which Nigeria is signatory to. We're calling on [the] government to investigate and fish out those who are behind such human rights violations, irrespective of who they are," Hayatu said.
Last month, observers said the presidential election in which the ruling party's Bola Ahmed Tinubu was declared the winner lacked transparency and didn't meet the expectations of most citizens.
Experts said there's heightened tension in many states, including Adamawa state where incumbent governor Ahmadu Fintiri of the People's Democratic Party and Senator Aishatu Ahmed-Binani of the All Progressive Congress are locked in a tough race.
Ahmed-Binani is the first woman with a realistic chance of being elected governor in Nigeria.