The army statement said the blasts were caused by a car bomb and an explosive device that went off near the army command buildings. It said "terrorists" in the area simultaneously opened fire randomly to terrorize people, adding that authorities were pursuing the gunmen. Syrian authorities regularly refer to rebels fighting to topple Assad's regime as terrorists.
The statement said a number of guards were wounded.
"I can confirm that all our comrades in the military command and defense ministry are fine," Information Minister Omran Zoubi told Syrian TV, which is located near the site of the explosion, in a telephone call.
"Everything is normal," he said. "There was a terrorist act, perhaps near a significant location, yes, this is true, but they failed as usual to achieve their goals."
Ambulances were rushed to the site as police sealed off the area to traffic and journalists. Traffic in other areas snarled as checkpoints were set up, blocking access to the capital from the suburbs.
Syria's unrest began in March 2011 when protests calling for political change met a violent government crackdown. Many in the opposition have since taken up arms as the conflict morphed into a civil war that activists say has killed nearly 30,000 people. Over the past few months, the rebels have increasingly targeted security sites and symbols of regime power in a bid to turn the tide in the fighting.
On July 18, rebels penetrated the heart of Syria's power elite, detonating a bomb inside a high-level crisis meeting in Damascus that killed three top regime officials, including Assad's brother-in-law and the defense minister. Other large blasts have targeted the headquarters of security agencies in the capital, killing scores of people this year.
On Tuesday, several bombs went off inside a Damascus school that activists said was being used by regime forces as a security headquarters. Several people were wounded.
Syria's conflict was the focus of attention as world leaders gathered at the U.N. General Assembly's annual meeting in New York this week.
U.N. Secretary-General Ban Ki-moon demanded international action to stop the war in Syria, telling a somber gathering of world leaders Tuesday that the 18-month conflict had become "a regional calamity with global ramifications."
Ban, declaring that the situation in Syria is getting worse every day, called the conflict a serious and growing threat to international peace and security that requires attention from the deeply divided U.N. Security Council.
That appears highly unlikely, however, at least in the near future.
Russia and China have vetoed three Western-backed resolutions aimed at pressuring Assad to end the violence and enter negotiations on a political transition, leaving the U.N.'s most powerful body paralyzed in what some diplomats say is the worst crisis since the U.S.-Soviet standoff during the Cold War.
In sharp contrast to the U.N. chief, President Barack Obama pledged U.S. support for Syrians trying to oust Assad - "a dictator who massacres his own people."