Three teachers are also missing following the attack on the school in the town of Tegina in the western state of Niger.
Abubakar Alhassan said he had spoken with the kidnappers who told him that the children were being fed and kept in a good condition.
He said the school had conducted a head count to ascertain the number of missing students.
Abductions carried out for ransom are widespread across Nigeria.
Earlier, Nigeria's President Muhammadu Buhari ordered security agencies to speed up their rescue efforts.