A spokesman for UN chief Antonio Guterres confirmed only that there was a "security incident", but gave no further details.
The West African country has seen several mass kidnappings over the years carried out either by bandits or militants, with the latest incidents sparking worries that no school is safe.
A group of gunmen kidnapped 317 girls from their boarding school in in the town of Jangebe, in Nigeria's Zamfara state last week.
"The abducted students and staff have regained their freedom and have been received by the Niger state government," Governor Abubakar Sani Bello says.
Local militia and residents say Boko Haram militants killed 10 people and injured 21 others with mortar shells in the volatile city.
Ruling party candidate Mohamed Bazoum is seen by many as the favourite after leading in the first round on December 27 with 39.3 percent of the vote. Polling stations opened at 0700 GMT and will close at 1800 GMT (8 am to 7pm) local time.
Nigeria’s president said he has dispatched security chiefs to coordinate a rescue operation for the students taken by the unidentified gunmen in Niger state.
Maiduguri city's three million residents plunged into darkness after a Daesh-linked militant group blew up transmission lines, in the third such attack in a month.
The fighting took place on Friday and Saturday in Salamat province, after cattle belonging to one herder ruined a field. The herders attacked as the farmers were taking the animals into an enclosure.
Four soldiers and seven hunters recruited to fight insurgents were killed when their vehicle hit landmines in northeastern Borno state.
Former interior minister Mohamed Bazoum, the ruling party's candidate, is the overwhelming favourite to succeed President Mahamadou Issoufou, who is stepping down after two five-year terms.
Boko Haram accused of storming a predominantly Christian village in Borno after security agencies warned the country of an increased risk of attacks during the Christmas holiday.
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