They say nine suicide bombers and two civilians died early on Friday.
It was the fiercest attack in months by Boko Haram on the city that is the birthplace of the Islamic insurgency.
Police say three female suicide bombers detonated vehicles parked at a truck station around midnight. The two civilians died there.
Self-defence fighters say soldiers later fired at gunmen on motorcycles escorting suicide bombers, killing at least six of the bombers.
Soldiers last year drove the Boko Haram insurgents from northeastern towns, but isolated attacks and suicide bombings continue.
The seven-year Islamic uprising has killed more than 20 000 people.