Abubakar Shekau
In the message, addressed to the leader of the Islamic State militant group to whom Boko Haram has pledged allegiance, Mr Shekau said he was still in command.
Mr Shekau identified himself as "governor" of the West Africa Province of the Islamic State group.
He had not featured in the group's recent videos, prompting speculation he had been killed or incapacitated.
Last week the Chadian president said Mr Shekau had been replaced.
The Nigerian army has dismissed the recording as irrelevant, saying it did not matter whether he was alive. or dead.
Mr Shekau described as "blatant lies" reports that he was no longer in charge.
"I am alive," he said, adding: "I will only die when the time appointed by Allah comes."
The eight-minute-long recording mocked a recent statement by the new Nigerian President Muhammadu Buhari that Boko Haram would be eliminated within three months.
Horrific attacks
Mr Shekau took over as the group's leader after its founder, Muhammad Yusuf, died in Nigerian police custody in July 2009.
Under his leadership Boko Haram has become more radical and has carried out more killings.
In numerous videos, Mr Shekau has taunted the Nigerian authorities, celebrating the group's violent acts including the abduction of the more than 200 Chibok schoolgirls in April 2014.
Last month, Mr Buhari said he would be willing to negotiate with the Boko Haram leadership for the release of the Chibok girls - depending on the credibility of those saying they represented the group.
A previous prisoner-swap attempt ended in failure.
Although momentum is gathering for a concerted regional offensive against the group, Boko Haram continues to carry out horrific attacks, not only in Nigeria but in its neighbours too, reports the BBC's Africa editor Mary Harper.
Boko Haram at a glance
Founded in 2002, initially focused on opposing Western-style education - Boko Haram means "Western education is forbidden" in the Hausa language
- Launched military operations in 2009
- Thousands killed, mostly in north-eastern Nigeria, abducted hundreds, including at least 200 schoolgirls
- Joined Islamic State, now calls itself "West African province"
- Seized large area in north-east, where it declared caliphate
- Regional force has retaken most territory this year,
- Profile: Boko Haram leader Abubakar Shekau
- Will new military base help defeat Boko Haram?
- Why Boko Haram remain a threat
He had not featured in the group's recent videos, prompting speculation he had been killed or incapacitated.
Last week the Chadian president said Mr Shekau had been replaced.
The Nigerian army has dismissed the recording as irrelevant, saying it did not matter whether he was alive. or dead.
Mr Shekau described as "blatant lies" reports that he was no longer in charge.
"I am alive," he said, adding: "I will only die when the time appointed by Allah comes."
The eight-minute-long recording mocked a recent statement by the new Nigerian President Muhammadu Buhari that Boko Haram would be eliminated within three months.
Horrific attacks
Mr Shekau took over as the group's leader after its founder, Muhammad Yusuf, died in Nigerian police custody in July 2009.
Under his leadership Boko Haram has become more radical and has carried out more killings.
In numerous videos, Mr Shekau has taunted the Nigerian authorities, celebrating the group's violent acts including the abduction of the more than 200 Chibok schoolgirls in April 2014.
Last month, Mr Buhari said he would be willing to negotiate with the Boko Haram leadership for the release of the Chibok girls - depending on the credibility of those saying they represented the group.
A previous prisoner-swap attempt ended in failure.
Although momentum is gathering for a concerted regional offensive against the group, Boko Haram continues to carry out horrific attacks, not only in Nigeria but in its neighbours too, reports the BBC's Africa editor Mary Harper.
Boko Haram at a glance
Founded in 2002, initially focused on opposing Western-style education - Boko Haram means "Western education is forbidden" in the Hausa language
- Launched military operations in 2009
- Thousands killed, mostly in north-eastern Nigeria, abducted hundreds, including at least 200 schoolgirls
- Joined Islamic State, now calls itself "West African province"
- Seized large area in north-east, where it declared caliphate
- Regional force has retaken most territory this year,
- Profile: Boko Haram leader Abubakar Shekau
- Will new military base help defeat Boko Haram?
- Why Boko Haram remain a threat