The statement was posted online six days after Iraqi officials told The Associated Press that Abu Bakr al-Baghdadi was wounded in an airstrike in Iraq. It was not clear whether the recording was made before or after the incident.
In the 17-minute recording, al-Baghdadi vowed to fight the "crusader campaign" to the bitter end.
"God has ordered us to fight," he said. "For that reason the soldiers of the Islamic State are fighting... They will never leave fighting, even if only one soldier remains. They will never leave fighting, because they reject humiliation."
The self-styled caliph called on Muslims to wage holy war everywhere, and to attack and kill "apostates" in Saudi Arabia and Yemen specifically.
An earlier audio recording from al-Baghdadi is believed to have inspired militants in Algeria to kill and behead a French national.