"The Islamic State group yesterday used bulldozers to destroy the Mar Elian monastery in Al-Qaryatain, in Homs province," said Syrian Observatory for Human Rights director Rami Abdel Rahman.
He said the militants demolished the Syriac Catholic monastery "on the pretext that it was used for worshipping others than God."
Photographs posted online by IS showed militants bulldozing parts of the monastery, although they did not appear to have completely destroyed the building with explosives as they have done with shrines and other religious buildings elsewhere.
The town lies at the crossroads between IS territory in the eastern countryside of Homs and points further west in the Qalamun area bordering Lebanon.
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The Observatory said that IS had released 48 of those it took captive when it overran the town, and had transferred another 110 to its stronghold of Raqa province.
The fate of the other 70 hostages was unclear.
The Mar Elian monastery dates back to the fifth century and is named for a Christian from Homs province who was martyred for refusing to renounce his faith.
In May, Syrian priest Jacques Mourad was abducted from the monastery by masked men as he prepared to receive residents of nearby Palmyra fleeing an IS advance.
Intolerant of any religious practice other than its own interpretation of Islam, IS has regularly destroyed religious buildings and icons in territory under their control.
They have also targeted statues, which they consider idolatrous, and grave markers, including those of Muslims.