The bombs targeted a security compound that was not far from the hotel where United Nations cease-fire observers are staying.
SANA, Syria's state news service, wrote that eight people died, including "law-enforcement members" and described the blasts as "twin explosions" that "hit Hanano Square and Carilton Street on Monday morning."
"The explosions also caused big material damage to residential buildings," SANA said.
The BBC said the bombs exploded next the Air Force and Military Intelligence headquarters, two of the multiple security branches that comprise the state's secret police and intelligence services. State TV "showed scenes of devastation, with big buildings partially collapsed, and streets full of rubble and wrecked vehicles. It also showed pools of blood left behind by some of the casualties."
Rocket-propelled grenades were launched at the central bank in Damascus today. The New York Times said four police were injured in another attack, and the rocket attack "slightly damaged" the bank building.