"About 30 suspected Boko Haram terrorists were killed in the battle which lasted several hours," Lieutenant Eli Lazarus, an army spokesman, said in a statement on Sunday.
Troops of the Joint Task Force (JTF) "engaged in a gun battle with the suspected terrorists" during a search-and-cordon operation on Boko Haram's hideout in Kandahar and around cemetery areas of Damaturu, the state capital, the statement said.
Ten suspected members of the group who were arrested during the raid are helping investigators to track other senior members of the group, added the statement.
Six rifles, 90 rounds of ammunition, several telephone sets were recovered during the raid. Knives, bows, arrows, daggers and three improvised explosive devices, which were detonated, were also confiscated, Lazarus said.
Patrick Egbuniwe, Yobe state police chief, said earlier on Sunday that troops shot dead four suspected members of the armed group following a raid on their hideout in Kandahar.
"We carried out the raid because of the incessant ambush on JTF patrol teams by Boko Haram gunmen in the area," he said.
Islamist extremists have been blamed for more than 1,400 deaths since 2010 as part of their attacks in northern and central Nigeria.
The JTF statement commended the support of Yobe residents and urged to give more information that will lead to the arrest of more suspected Boko Haram members.
"JTF further requests that people should remain calm and go about their lawful activities as efforts are geared towards ensuring the safety of lives and property," added the statement.
Last month in Damaturu, the military said it killed 35 suspected Boko Haram members in fierce gun battles. Some 60 people were also arrested there following a door-to-door sweep in several neighbourhoods.
A number of security personnel have also been arrested over links to Boko Haram.
The arrests came after JTF soldiers in the northeastern city of Maiduguri arrested an immigration officer, Grema Mohammed, for allegedly being an active member of the group, a military spokesman had said.
The JTF is a special unit made up of troops drawn from the armed forces, the police and the state security service.