The offensive followed intelligence that the extremist group planned to attack the city again, said the deputy police spokesman of Yobe state, of which Damaturu is the capital.
“Security operatives were able to discover a plan by Boko Haram hoodlums to launch attacks in the city,” said Gbadegesin Toyin.
The Joint Task Force (JTF) military unit “located their positions… they cordoned off these positions and engaged the gunmen in a shootout,” he added.
He said soldiers fired mortar rounds at the Islamist militants, who responded with gunfire and also threw improvised explosive devices, adding that the fighting was continuing.
The violence was most heavily concentrated in the Nyanya and Obasanjo Estates areas of the city.
“Explosions and gunshots have been going on in this neighbourhood (Nyanya) for over an hour,” said Abdullahi Musa, a civil servant.
Another resident offered a similar account.
“We are frightened due to the blasts and gunfire. We don’t know what is happening because we are indoors… We pray we stay safe,” said Safiya Mahmud, a housewife, earlier.
Nigerian authorities on June 19 slapped a round-the-clock curfew on Damaturu, after suspected Boko Haram Islamists launched coordinated gun attacks on targets around the city.
The curfew was partially relaxed two days later after soldiers and police reclaimed control of the streets in an offensive that left at least 40 people dead, including 34 alleged Boko Haram members.
The ban on movements was further eased on Monday, but Damaturu residents are still forced to remain in their homes between 6:00 pm and 7:00 am.
Damaturu has repeatedly been hit by the radical Islamist group, responsible for more than 1,000 deaths since the middle of 2009 in Africa’s most populous nation and largest oil producer.
Yobe state borders the extreme northeastern state of Borno, where the capital Maiduguri is considered Boko Haram’s base.
The Islamist group’s insurgency, concentrated mainly Muslim north, has frequently targeted the security forces, though the Islamists have attacked churches and other symbols of authority.
The government’s response to Boko Haram in past months has included heavy-handed military raids, which had angered residents of hard-hit areas and failed to stop the extremists.
Last week, President Goodluck Jonathan fired his national security adviser and defence minister, amid intensifying criticism of his administration’s response to the Boko Haram threat.
The Islamist group initially said it was fighting for the creation of an Islamic state, but its demands have since shifted repeatedly. It is believed to have a number of factions, including a main Islamist wing.
Many say deep poverty and frustration in the north have been main factors in creating the insurgency.