It was not immediately possible to verify the claim.
In the statement signed by the "communication service of the province of Barqa", the group accused the two Tunisians, Sofiene Chourabi and Nadhir Ktari, of having worked for "a satellite channel that fights religion".
Barqa is the ancient name of a region in eastern Libya where IS is thought to have gained a foothold.
A picture showed the two young men alongside an armed man in fatigues, his face covered.
Their disappearance came after the pair, who were working in Libya without authorisation, were detained by an armed group days earlier but released.
Libya has been engulfed by chaos since the 2011 NATO-backed uprising that toppled and killed veteran dictator Moamer Kadhafi, with two rival governments and a host of militias now vying for territory.
IS has seized swathes of Iraq and Syria, declaring a "caliphate" and committing widespread atrocities, including the beheading of Western hostages.
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