State media and residents said the explosions struck the General Staff Command Building (Hay'at al Arkan) in the Umayad Square in central Damascus, which is one of the top military headquarters in Syria.
There was no immediate word on casualties.
The Syrian information minister said the attack had caused "only material damage" and that security forces were chasing "armed terrorists" - a term the authorities use to refer to insurgents waging a violent uprising to oust Syrian President Bashar al-Assad.
Gunfire and other smaller blasts could be heard after the explosions, as well as the sound of ambulance sirens. Many roads in the centre of the capital were blocked, residents said.
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