"The Joint Task Force has succeeded in killing 35 Boko Haram terrorists in shootouts between Sunday evening through Monday," said Lieutenant Lazarus Eli, a military spokesman in Yobe state, of which Damaturu is the capital.
A round-the-clock curfew was imposed in the city late Saturday, ahead of the operation that also led to the arrest of 60 suspected Boko Haram members.
The curfew has been relaxed and residents are now allowed out of their homes from 7:00 am to 10:00 pm (0600 GMT to 2100), Eli said. The ban on movements in Yobe`s economic capital of Potiskum has also been eased.
Military forces went door-to-door through three Damaturu neighbourhoods beginning late Sunday and engaged militants in "a fierce exchange of gunfire" through to the early hours of Monday morning, the spokesman added in a statement.
Two soldiers were injured in the fighting.
Damaturu has been hit hard by the radical Islamist group which is blamed for more than 1,400 deaths in Africa`s most populous nation since 2010.
Running gun battles between suspected Boko Haram members and the security forces in June put the city under lockdown, with some stranded in their places of work for several days unable to access food and water.
A list of weapons that Eli said were recovered from Boko Haram hideouts included dozens of guns, explosive devices and hundreds of rounds of ammunition as well 32 arrows and two swords, among other items.
Violence blamed on Boko Haram had ebbed in recent weeks, but a suicide blast at a church in the northern city of Bauchi on Sunday which killed a woman and a child resembled attacks previously claimed by the group. (M014)
Editor: Kunto Wibisono
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