An email statement attributed to the sect and obtained by The Associated Press on Thursday said it launched the attacks in Damaturu.
The attacks began Monday evening with blasts targeting police and military targets in the Yobe State capital, authorities said.
Gunfire echoed across the city for hours, spilling into Tuesday afternoon. One resident said at least two schools were torched.
The attacks killed at least 34 civilians and six security officers including four policemen and two soldiers, according to Yobe State police Chief, Patrick Egbuniwe.
The casualty figure could be higher since Muslim mourners often quickly bury their dead without alerting authorities.
“The terrorists are trying to show that they can’t be stopped,” Egbuniwe said soon after the attacks started.
The Islamist Boko Haram sect, whose name means “Western education is sacrilege” in the Hausa language, is waging an increasingly bloody fight with Nigeria’s security agencies and public. More than 640 people have been killed in violence blamed on the sect this year alone, according to an AP count.
“We assure all that the success of the Damaturu operation is really a sign that very soon, Allah will give us the chance of overthrowing this unjust and heathen government and replacing it with an Islamic system which is just,” the statement attributed to the group said in the local Hausa language.