The statement said: "The President wishes to assure all Nigerians that there is no cause for worry".
This release brings the total number of girls released by the group to 103 out of the 276 abducted - about 60 escaped from captivity at various times, leaving 113 girls still in the captivity of the terrorists.
Adesina said Buhari had planned to leave in the afternoon on Sunday, but had to wait to receive the 82 Chibok schoolgirls, who were freed by their Boko Haram abductors. The official spoke on condition of anonymity as he was not authorized to speak to reporters on the matter. A military source said three Boko Haram commanders had been freed in an exchange, but declined to give further details.
Parents of the schoolgirls were waiting for a government list of names of those who had been freed.
In this photo released by the Nigeria State House, Nigeria's President, Muhammadu Buhari, left, meets with Chibok school girls recently freed from Nigeria Extremist captivity in Abuja, Nigeria, Sunday, May.
Martha Mark says two of her daughters are missing. He emphasized, though, that he considered all 82 of the girls to be his daughters "because a lot of them worship in my church".
Some parents did not live long enough to see their daughters released, underscoring the tragedy of the three-year saga.More news: Tillerson meets ASEAN ministers to seek support on North Korea
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Pernille Ironside, acting representative of Unicef Nigeria, told Sky News: "These girls have faced horrific and unspeakable crimes and experiences".
"So when you do have individuals that are being released back into the group, any impact that they may have in enhancing Boko Haram's operational capabilities will more than likely be limited to the specified area where they are deployed, as opposed to having a wide impact on the trajectory of the insurgency, " he said.
"They develop Stockholm syndrome, identify with captors and want to remain", said Akilu, who has run deradicalisation programs for Boko Haram militants and women abducted by them.
The release follows the freeing of a first group of 21 Chibok schoolgirls in October.
It was unclear if numerous parents in the remote northeastern town of Chibok had seen the list of names or if any would travel the almost 900 kilometers (560 miles) to the capital of Abuja to see their daughters who were abducted by the Boko Haram militant group.
It is unclear if the government has made other attempts to let them know if their daughters are now safe.
Amnesty International's Nigeria office said the girls should not have to endure a lengthy government detention or a "publicity stunt" but instead should be given privacy to recover.