"We do not know if the Chibok girls can be rescued. Their whereabouts remain unknown. As much as I wish to, I cannot promise that we can find them," he said in a statement.
"But I say to every parent, family member and friend of the children that my government will do everything in its power to bring them home."
Buhari's statement on the first anniversary of the girls' abduction from the northeastern state of Borno on April 14 last year contrasts markedly with that of outgoing President Goodluck Jonathan and his government.
Jonathan, who was widely criticised for failing to respond to the crisis, has repeatedly said the girls will be returned, without offering any details.
But Buhari, who defeated Jonathan in a historic election two weeks ago after campaigning against the president's record on security, said there was a need for "honesty" about the girls' fate and the insurgency.
The 72-year-old promised: "When my new administration takes office at the end of May, we will do everything we can to defeat Boko Haram.
Buhari, a former military ruler who has promised a tough line in tackling the insurgency, said the kidnapping had "rightly caused outrage" in Nigeria and around the world.
"Today is a time to reflect on the pain and suffering of the victims, their friends and families. Our thoughts and prayers, and that of the whole Nigerian nation, are with you today," he added.
He also pledged to improve education, particularly for young girls in the impoverished north, once Boko Haram was defeated and normality returned to the remote region.
"We stand united in our pledge to resist terror in Nigeria -- not just through military means but also through the power of opportunity and the hope of a better future for all.
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