"Two terrorist car bombs driven by suicide bombers detonated at the entrance of Ummayed Square," the official SANA news agency and state television reported, without specifying if there were any casualties.
The blasts went off near the building of the national broadcaster, with a state television reporter on the ground saying a concrete barrier outside it had been damaged but the facility was largely intact.
Footage of the scene broadcast by the government-run Al-Ikhbariya TV showed fires burning and smoke rising over the site as firefighters worked to put them out.
The explosions occurred only a few kilometres from the hotel where a team of international experts from the Organisation from the Prohibition of Chemical Weapons and the United Nations are staying.