Fighting around the capital city has intensified over the past week, prompting predictions among Western opponents of Mr Assad that an endgame is approaching in a 20-month-old conflict that has killed 40,000 people.
Syria's Government, however, says the army is driving rebels back from positions in the suburbs and outskirts of Damascus.
But a spokesman for the Damascus Military Counci said:. "The rebel brigades who have been putting the airport under siege decided yesterday that the airport is a military zone."
Meanwhile, the UN Secretary-General Ban Ki-moon said yesterday he was not aware of any confirmed reports that Mr Assad was preparing to use chemical weapons but if he did so it would be an "outrageous crime".
"I know that many world leaders have added their voices urging him not to use it and warning him that it will create huge consequences," he added.
Also yesterday, the Dutch Government agreed to send two Patriot missile systems to Turkey after Ankara asked Nato for assistance in defending its border with Syria.