Abu Bakr al-Baghdadi has been appointed caliph by the jihadist group, which has seized large swathes of Iraq and Syria.
The video appears to have been filmed on Friday during a sermon at the al-Nouri Mosque in Mosul, northern Iraq.
The footage surfaced on Saturday amid reports that he had been killed or wounded in an Iraqi air raid.
It was not clear when the attack was supposed to have taken place.
In the sermon, at Mosul’s most famous landmark, Abu Bakr al-Baghdadi praised the establishment of the “Islamic state”, which was declared by ISIS last Sunday.
Experts say the reclusive militant leader has never appeared on video before, although there are photographs of him.
“Appointing a leader is an obligation on Muslims, and one that has been neglected for decades,” he said.
Abu Bakr al-Baghdadi also said that he did not seek out the position of being the caliph, or leader, calling it a “burden”.
“I am your leader, though I am not the best of you, so if you see that I am right, support me, and if you see that I am wrong, advise me,” he told worshippers.
Captions in the video referred to Abu Bakr al-Baghdadi as “Caliph Ibrahim”, a name he has used since the group unilaterally declared him leader of an “Islamic state” last Sunday.
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