Eyewitnesses say hundreds of militants attacked several areas of the city of Maiduguri, starting early on Monday.
A 24-hour curfew has been imposed in Maiduguri. Its civilian airport was also briefly closed.
Thousands of people have been killed since 2009, when Boko Haram launched its campaign to install Islamic law.
In May, a state of emergency was declared in Borno state, of which Maiduguri is the capital, as well as two neighboring states, while there has been a massive military deployment to the worst-affected areas.
Ministry of Defence spokesman Brig Gen Chris Olukolade said in a statement that two helicopters and three decommissioned military aircraft had been “incapacitated” during the attack which had been repelled.
He said some army bases had also been targeted, while 24 insurgents had been killed and two soldiers wounded.
Local residents told the AFP news agency that hundreds of heavily armed Islamist gunmen besieged the air force and army bases, razing buildings and setting shops and petrol stations ablaze.
“I saw two air force helicopters burnt,” a local official told AFP.
Bomb and gun attacks were carried out in Maiduguri, an AFP reporter in the city said.
A resident said: “We heard women and children in the barracks crying and wailing. At the gate, I saw some vehicles destroyed and the checkpoint there in shreds.”
There are reports of military checkpoints being attacked in different parts of the city.
Some eyewitnesses told the AP news agency they had seen bodies with their throats slit.
Others said several vehicles had been driven out of the air base carrying the bodies of victims.
Government and military officials said scores of people may be dead, AP reported.
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