The unidentified speaker calls Nigeria, Cameroon, Chad and Niger, who have been battling the Islamists, "the lying coalition partners".
"Most of our territory is still under our control," said the speaker, whose face is not shown in the 10-minute message posted on YouTube.
The video bears the logo "Islamic State in West Africa" and follows the Nigerian militants' pledge of allegiance in March to the IS group, that has overrun large parts of Syria and Iraq.
He had featured prominently in most of the group's videos over the last three years and his absence in the latest message will likely stir further debate on his whereabouts or possible death.
Nigeria's military has previously claimed to have killed Shekau and described him as a composite character, with the role of "Shekau" filled by various similar-looking insurgents at different times.
The speaker in the new message appears in front of two pick-up trucks, with four other gunmen visible in the background.
An AK-47 rifle rests on his chest as he seeks to rebuke the claims of successes made in recent weeks by the coalition.
"The armies claim through the media that they captured our towns and that they assaulted Sambisa (forest) and defeated us," he said, referring to the bushland area in Nigeria's northeast Borno state that has been an Islamist stronghold.
"I swear by Allah that I am talking right now from Sambisa... Here in Sambisa you can travel more than four to five hours under the black flag of Islam by car or by motorbike," he added.
"President of Nigeria Jonathan" is mentioned, referring to Goodluck Jonathan, who handed over power to Muhammadu Buhari on Friday, two months after the latter's victory in elections on March 28.
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