Buhari ordered a "massive" deployment of military and intelligence assets to restore normalcy to Nigeria's northwest, National Security Adviser Babagana Monguno told journalists in Abuja after a security council meeting.
The government "will not allow this country to drift into state failure," he said in response to the abductions. "We are not going to be blackmailed."
A series of school abductions in recent months has led many Nigerians to worry that regional authorities are making the situation worse by letting kidnappers go unpunished or paying them off.
Buhari said earlier on Tuesday that the practice of paying ransoms had encouraged kidnappers. The state government in Zamfara has denied paying a ransom but said it offered the kidnappers amnesty and help settling.
Zamfara is home to large gold deposits, with a legal mining industry operating alongside illegal mines that the authorities say have fuelled violence. The impact of a no-fly zone was difficult to assess as the state has no major airport.
Armed groups have plagued the state and its neighbours in recent years, kidnapping for ransom, looting and destroying communities and murdering civilians. Security forces' attempts to halt their rampage have met with little success.
(Reporting by Felix Onuah in Abuja; Writing by Paul Carsten; Editing by Peter Graff)
