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The head of the Syrian Observatory Rami Abdel Rahman said the explosion was heard across the capital.
"The blast was huge and could be heard in Damascus," he said.
The dawn explosion has also been reported by other activists' networks.
Activist-operated Diary of a Mortar, which reports from Damascus, said the explosion was followed by flames rising above the area. A pro-government site Damascus Now said the explosion was near the city's Seventh Bridge, which leads to the airport road.
Earlier, some social media users reported air strikes at Syria's Mezzeh Military Airport in Damascus as well as at the international airport.
On Twitter earlier, The Times of Israel said the explosion could have been an air strike by Israel. It also reported explosions at the military airport.
Al Jazeera, quoting witnesses and "several activists networks", said there were two blasts, at the airport and at Mezzeh Military base.
In January, the Syrian army command said Israel had fired rockets at a major military airport west of Damascus, and warned Israeli authorities of repercussions for what it called a "flagrant" attack.
Then, Syrian state television quoted the army as saying several rockets were fired from an area near Lake Tiberias in northern Israel just after midnight which landed in the compound of the airport, a major facility for elite Republican Guards. Israel in the past has targeted positions of Lebanon's powerful Hezbollah group inside Syria, where the Iranian-backed militant Islamist group is heavily involved in fighting alongside the Syrian army.