Sunday attributed to him by security experts.
In the eight-minute Hausa-language message, Abubakar Shekau rebuffed claims by Chadian leader Idriss Deby that he had been replaced and called the president a "hypocrite" and a "tyrant".
"It is indeed all over the global media of infidels that I am dead or that I am sick and incapacitated and have lost influence in the affairs of religion," he said in the recording released on social media.
"It should be understood that this is false. This is indeed a lie. If it were true, my voice wouldn't have been heard, now that I am speaking."
Deby declared on August 12 that efforts to combat neighbouring Nigeria's Boko Haram jihadists had succeeded in "decapitating" the group and would be wrapped up "by the end of the year".Deby told reporters in the capital N'Djamena Boko Haram was no longer led by the fearsome Shekau and that his successor, whom he named as Mahamat Daoud, was open to talks.
"Gratitude be to Allah and with his help, I have not disappeared. I am still alive and I am not dead. And I will not die until my time appointed by Allah is up," Shekau said in the message.
The SITE Intelligence Group verified the authenticity of the message, and an AFP correspondent with extensive experience of reporting Boko Haram said it exactly resembled Shekau's voice in previous recordings.
- Taunts -
Shekau's absence from Boko Haram videos in recent months has fuelled speculation that he might have been killed or wounded.
He has not spoken publicly since he pledged allegiance to the Islamic State (IS) group in an audio recording released on March 7.The jihadist commander refers to himself in the new recording for the first time as "leader of the west Africa wing" of IS and pays homage to its leader Abu Bakr al-Baghdadi, referring to him as the "Caliph of Muslims".
He taunted Nigeria's President Muhammadu Buhari, who came to power on May 29 vowing to crush Boko Haram and ordered his military chiefs last week to end the insurgency within three months.
"This ostentatious person, a liar -- I mean Buhari, who raised arms to crush us in three months. You Buhari, why didn't you say in three years?" Shekau demanded.
"We will certainly fight you by the grace of Allah until we establish Allah's law everywhere on Earth."
Boko Haram has been waging a six-year uprising against the Nigerian state, which has claimed more than 15,000 lives.
The jihadists have repeatedly extended their northeastern insurgency into border areas of Cameroon, Chad and Niger.In recent weeks suicide bombers, many of them women, have staged several attacks in Nigeria, Cameroon and Chad.
The four countries, plus Benin, have pledged troops towards a regional 8,700-strong force aimed at ending the insurgency and due to deploy within days.
- 'Global terrorist' -
Speculation about Shekau's condition -- and even his true identity -- has been rampant in Nigeria for years.
The wanted Islamist leader's whereabouts are unknown, but he has in the past made himself heard whenever he has been proclaimed dead.
The original Abubakar Shekau -- the son of poor farmers who became radicalised in a series of theological schools before taking over Boko Haram in 2010 -- actually died months, or possibly several years ago, according to the security services.
But the United States and other experts have questioned the credibility of that claim.
"Here I am, alive. I will only die the day Allah takes my breath," the insurgent leader, who has been sanctioned by the UN Security Council and declared a "global terrorist" by the United States, said in a video released in October last year.
He issued a similarly boastful denial in 2013 after the military claimed he may have died from a gunshot wound.