Maamoun Abdulkarim told Reuters that sources in Palmyra had confirmed the destruction of three tombs including that of Elahbel, built in 103 AD, which he said was four storeys high and had an underground floor.
Islamic State militants blew up two temples at the Roman-era, UNESCO World Heritage site, which it has controlled since capturing Palmyra from Syrian government control in May.
The group considers the buildings sacriligeous.
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