The video obtained by AFP on Monday also depicts women and children apparently being held hostage.
It features Abubakar Shekau, declared a global terrorist by the United States, seated on a rug with a kalashnikov resting behind his right shoulder.
"We are the ones that carried out the Bama attack," Shekau said in the Hausa language, referring to the May 7 assault that killed 55 people, mostly soldiers and police.
"We also carried out the attack in Baga," he further said of the April 16 raid in the town near Lake Chad that sparked clashes with soldiers which killed nearly 200.
Nigeria's military has been accused of causing scores of deaths in the Baga violence by deliberately setting fires that razed thousands of homes.
"It was you, the security agents that went into town the following day and burnt homes and killed people at will," Shekau said.
The military has fiercely denied the reported abuses by its soldiers, insisting that only 37 people died in the Baga violence, including 30 suspected Islamists.
Some seven minutes into the 12-minute video message, the screen splits, showing Shekau on the left with a group of unidentified women and children on the right.
The Islamist leader claimed this group is being held hostage in retaliation for the wives and children of Boko Haram members detained by the military.
Boko Haram has never before boasted about the kidnapping of Nigerian women and children.
"As long as we do not see our women and children we will never release these women and children," Shekau said.
The group set out a similar condition for the release of seven members of a French family who were kidnapped in February in Cameroon near the Nigerian border. The Moulin-Fournier family were released last month.
Before claiming the French abductions, Boko Haram had not widely been associated with kidnappings.
Their attacks, which have killed hundreds since 2009, have included suicide blasts as well as co-ordinated gun and bomb assaults on the security forces and other symbols of authority.
The recent attacks in the northeast have raised concern about the increasingly brazen tactics used by the insurgents, who have said they are fighting to create in Islamic state in mostly Muslim northern Nigeria.
In Bama, they stormed the commercial centre in a convoy of seven vehicles, launching coordinated pre-dawn attacks on the military, police and several government buildings.
Under pressure over his apparent inability to contain the violence, President Goodluck Jonathan created a panel to seek an amnesty deal with the insurgents.
In his latest video, Shekau re-stated his opposition to any such pact.
"You talk of dialogue …You are free to say whatever you want to say but we will never stop our struggle," he said.
While Shekau's hardcore Islamist loyalists may resist a peace deal, analysts believe that Boko Haram is fractured, with some camps possibly open to amnesty.
The Boko Haram conflict is estimated to have cost 3 600 lives since 2009, including killings by the security forces.
The images of Shekau in the latest video resemble those previously released by the group and the message was distributed by email, in a manner consistent with earlier Boko Haram messages. – AFP