In the eight-minute Hausa-language message, Abubakar Shekau denied claims by Chadian leader Idriss Deby that he had been replaced and calls 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 says 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 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 says in the message.