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 terrorist 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 northeastern 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.

Shuwa, 79, was a top adviser to Yakubu Gowon, the former military head of state who led Nigeria during the 1967-70 Biafra civil war that left more than one million dead, including many from starvation.

He also served as a senior leader in the 1975-76 junta of Murtala Mohammed.

In an interview at his home in May, Shuwa pulled out a handgun that he said he carried for his own protection and told AFP that anyone could potentially be targetted by Boko Haram in the violence-torn city.

Boko Haram has carried out scores of targeted assassinations in addition to bombings and shootings. The insurgency has left some 3,000 people dead since 2009, including killings by the security forces.

The group has claimed to be seeking an Islamic state in Africa's most populous nation and largest oil producer, though its demands have repeatedly shifted.

It is also believed to include a number of factions with differing aims in addition to criminal gangs and imitators who have carried out violence under the guise of the group.

At the same time, Nigeria's military has been accused of widespread abuses in its bid to crack down on the Islamists, including killings of civilians, burnings of homes and unlawful detentions.

Both Human Rights Watch and Amnesty International recently issued reports accusing the military of major abuses in response to Boko Haram.

Human Rights Watch alleged that Nigerian security forces as well as Boko Haram may both be guilty of crimes against humanity.