Palmyra, one of the Middle East's most spectacular archaeological sites and a UNESCO World Heritage site, sits near the modern Syrian city of the same name.
Activists said the militants used explosives to blow up the Baalshamin Temple on its grounds, the blast so powerful it also damaged some of the Roman columns around it.
The Britain-based Syrian Observatory for Human Rights said yesterday night that the temple was blown up a month ago.
Both relied on information for those still in Palmyra and the discrepancy in their accounts could not be immediately reconciled, though such contradictory information is common in Syria's long civil war.
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The Sunni extremists, who have imposed a violent interpretation of Islamic law across their self-declared "caliphate" in territory they control in Syria and Iraq, claim ancient relics promote idolatry and say they are destroying them as part of their purge of paganism. However, they are also believed to sell off looted antiquities, bringing in significant sums of cash.
The temple dates to the first century and is dedicated to the Phoenician god of storms and fertilising rains.
The head of UNESCO, Irina Bokova, said Friday that Islamic State extremists in Syria and Iraq are engaged in the "most brutal, systematic" destruction of ancient sites since World War II" a stark warning that came hours after militants demolished the St. Elian Monastery, which housed a fifth-century tomb and served as a major pilgrimage site.