Nigeria's military on Thursday claimed to have killed a Boko Haram commander behind the recent high-profile assassination of a retired general in a "major offensive."

"During the offensive and in a counter-attack, a major commander of the Boko Haram terrorists sect commanding the northwest and the northeast, Ibn Saleh Ibrahim, with some of his commanders and foot soldiers, were killed by (our) own operation troops," a military statement said of Thursday's operation in the city of Maiduguri.

"The late Ibn Saleh was confirmed to be responsible for the recent assassination of Civil War hero, the late General Mamman Shuwa, through the orders of the leader of the Boko Haram terrorists, Abubakar Shekau."

It added that the operation was still ongoing and that weapons and explosives had been recovered.

Nigeria's military has however frequently exaggerated its successes against Islamist extremist group Boko Haram, whose insurgency in the country's northern and central regions has left hundreds of people dead.

The claim from the military could not be independently verified.

The statement called it a "major offensive" that included armoured vehicles and helicopters.

The retired general, a key figure in the 1960s civil war, was shot dead on November 2 by what was then described as unknown gunmen at his home in Maiduguri, the city hardest hit by the Islamist insurgency.