In the 24-minute audio, Abu Bakr al-Baghdadi said the US won't come to fight the extremists because "their hearts are full of fear from the mujahideen".
The message was Baghdadi's first since May, and comes amid battlefield setbacks that ISIS has recently faced.
The authenticity of the recording could not be confirmed. It appeared to be Baghdadi's first public address since May, and it followed reports that he had been either killed or gravely wounded by airstrikes.
In the message, Baghdadi acknowledged escalating pressure on the Islamic State but framed it as worldwide attack by "disbelievers" against Muslims.
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"America and its allies dream of destroying the caliphate through their proxies and henchmen, and whenever an alliance of theirs fails or a tail is cut, they hasten to establish another, until they recently declared the Salouli (Saudi) alliance that was falsely called Islamic," US media quoted Baghdadi as saying.
"We promise you, God permitting, that whoever participates in the war against the Islamic State will pay the price dearly."
"Soldiers of the Islamic State be patient because you are on the right path," Baghdadi said, adding "Be patient, because God is with you."
He also threatened Israel saying: we haven't forgotten you" and "we are getting closer to you" every day. To Israeli Jews, he said that they "will hide behind trees and stones" from the ISIS.
And while he referred to several recent developments, including the entrance of Russia's military into the Syrian war and the claim by Saudi Arabia to be forming a military coalition of Muslim countries, Baghdadi did not refer to recent mass killings in Paris and San Bernardino that were connected to the Islamic State.