The network aired footage of the airport, along with interviews of employees and passengers, to show that operations were normal.
The captured swath stretches from the town of Harran Al-Awameed, almost within a mile of the airport, up to the Damascus suburb of Deir Asafeer and includes a captured military helicopter airport and a road to connect them all, the military council said.
Despite government bombardments, which have rained death and destruction indiscriminately from above for months upon rebel stronghold neighborhoods, revolutionary fighters have gained ground.
They have captured military bases, driving out regular army troops, seizing their heavy weaponry and turning it back on them -- including anti-aircraft guns and missiles.
In the last week, rebels claim to have shot down one plane and two helicopters in Syria's north. CNN's Arwa Damon went to the crash site of the plane Wednesday, and saw chunks of metal being carted off by locals.
U.S. Secretary of State Hillary Clinton on Friday called for ongoing support of the opposition's "current momentum" via non-military aid to Syrian rebels in a speech in Washington. The United States and many of its allies have thrown their support behind the rebel movement and openly advocate the overthrow of Assad's government.
U.N. Secretary General Ban Ki-Moon urged the international community Friday, "in particular the Security Council," to pull together.
Council members China and Russia, which are allies of Assad, are at loggerheads over the handling of the crisis with the other permanent members France, Britain and the United States, which oppose Assad.
Ban said he would soon visit Syrian refugees who have fled over the borders to neighboring countries.
More than 42,000 people have died in the Syrian conflict since the uprising began in March 2011, according to opposition activists. CNN cannot confirm claims by the government or the opposition because of government restrictions that prevent journalists from reporting freely within Syria.