Soldiers supported by two fighter jets intercepted the militants who were in 20 pick-up trucks at Dungulbe village, seven kilometres (four miles) from the city, and engaged them in fierce fighting.
"The fighter jets are pounding the enemy position while ground troops are engaging them," said a military officer in the city, who asked not to be identified, in an account supported by residents.
"The operation is still ongoing but the terrorists have suffered serious losses and are in disarray," the officer added.
A spokesman for the Bauchi state governor said an indefinite, round-the-clock curfew had been imposed on three areas because of the fighting.
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"The state government has put a 24-hour curfew in Bauchi, Kirfi and Alkaleri local governments as a result of the security breach by Boko Haram," Danlami Baban-Takko said.
"The curfew was imposed indefinitely... To enable security agencies to restore normalcy in the affected areas.
"By this curfew, residents of the three affected local governments are to remain in their homes until further notice."
"The curfew was only an attempt by the PDP (Peoples Democratic Party) to tinker with the results of the elections," he claimed.