An “intelligence report” showed that Abubakar Shekau, the leader of the Boko Haram group, may have died between July 25 and August 3, Lt-Col Sagir Musa said.
Boko Haram, which has waged an insurgency in Nigeria since 2009, has not commented on the statement.
The US had put a bounty of $7 million on Abubakar Shekau’s head.
The intelligence report suggested that Abubakar Shekau was shot on June 30, when soldiers raided a Boko Haram base at Sambisa Forest in north-eastern Nigeria.
“Shekau was mortally wounded in the encounter and was sneaked into Amitchide – a border community in Cameroon for treatment… It is greatly believed that Shekau might have died between 25 July to 3 August 2013,” Sagir Musa said.
A video of Abubakar Shekau released on August 13 was “dramatized by an imposter to hoodwink the sect members to continue with the terrorism”, he added.
On August 14, the military said it had killed Boko Haram’s second-in-command, Momodu Bama, also known by his alias “Abu Saad”.
Correspondents say there is no independent confirmation of Abubakar Shekau’s or Momodu Bama’s death.
Thousands of people have died since Boko Haram began its insurgency in 2009.
A claim in 2009 that Abubakar Shekau had been killed turned out to be untrue, they add.
He became leader of Boko Haram after its founder, Muhammad Yusuf, died in police custody in the same year.
The insurgency became far more brutal under Abubakar Shekau’s leadership, with Boko Haram carrying out a wave of bombings and abductions, including that of foreigners, in its campaign to create an Islamic state across Nigeria, correspondents say.
In May, Nigeria’s President Goodluck Jonathan declared an emergency in three north-eastern states, saying the group threatened the country’s existence.
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