It was the second consecutive day that bombs, apparently planted by rebels, hit the capital, highlighting insurgents' ability to strike at the heart of the government of President Bashar Assad.
The attacks come as the United Nations General Assembly has been debating the crisis in Syria, though a deeply divided U.N. has failed in efforts to broker a cease-fire.
The official state news service said two "“terrorist explosions" took place near the headquarters, where the army and air force commands are situated, in central Umayyed Square.
The bustling square is a hub of government and state media offices in the core of Damascus.
The state news agency quoted the information minister, Omran Zoubi, as saying that "all military commanders and media persons are safe ... the terrorist explosions were confined to material damages."
One of the two bombs was placed "inside the fence" of the building, the state news agency reported.
A thick plume of black smoke rose from the military compound a few minutes after the first blast, which went off at about 7 a.m. Damascus time. The huge plume of smoke soon turned gray and towered above the city.
A photograph circulated on the Internet showed what appeared to be flames coming from a building in the vicinity of the military headquarters.
A second, less powerful explosion went off about 10 minutes after the initial blast, residents reported.
Small-arms fire and the sound of sirens could be heard following the blasts. Authorities reportedly blocked all streets leading to and from Umayyed Square.
Residents reported shattered windows and paint peeling from their homes from the force of the initial blast. Many remained indoors and kept their children from attending school.
Iran's English-language Press TV reported Wednesday that one of its correspondents was killed and its bureau chief was injured while covering the blasts in Damascus. Press TV said Maya Nasser was killed by sniper fire and that Hussein Murtada, bureau chief in Damascus for Press TV and Iran's Arabic-language Al-Alam TV, was injured "by insurgents."
The explosions come a day after a pair of blasts hit a school complex used by the military. The government reported seven injuries but no fatalities in the bombing. The opposition said many military personnel were killed.
The series of bombings appears to be part of an opposition strategy to demonstrate rebels' continued capacity to strike in the capital. The government has proclaimed that its forces have regained complete control of Damascus following fierce clashes in July across various districts of the capital.
Government troops using tanks, artillery and aircraft assaulted rebel strongholds throughout the city in July and August. The offensive pushed opposition fighters into the suburbs and other outlying areas, where authorities have been pursuing them.
A number of explosions, including car bombs, have rocked the Syrian capital since late last year. A bomb planted inside a security headquarters in Damascus in mid-July killed four of Assad's top security aides, including his brother-in-law, the government said.
The 18-month rebellion against Assad's government is estimated to have left more than 20,000 dead.
Fighting rages on in various areas of the country, including the northern city of Aleppo, the central city of Homs and the eastern city of Dair Elzur. Rebels are fighting to oust Assad, whose family has ruled Syria for more than 40 years.
Assad blames the violence on a "foreign conspiracy" stoked by neighboring Turkey and various Persian Gulf nations and employing Islamic militants recruited from abroad.
-- Patrick J. McDonnell. A special correspondent in Damascus contributed.
Photo: A column of smoke rises from the military command headquarters in Damascus, Syria, after a pair of explosions. Credit: EPA