Checkpoints on the main artery have changed hands several times since Wednesday, when the opposition fighters started their campaign for the seat of President Bashar al Assad's power.
A rebel fighter yesterday said opposition forces had overrun al Adnan checkpoint in Jobar, north-east of Damascus.
The British-based Observatory for Human Rights said that while the fight for the highway continues, government troops regained control of the area on Saturday after using fighter jets to bomb rebel positions.
Syrian troops backed by warplanes had battled the rebels for control of the key road after opposition forces cut the strategic route as part of what they say are efforts to lay the groundwork for an eventual assault on the capital.
Rebels have been on the offensive in Damascus since launching a series of attacks on government positions last week. They brought their fight to within a mile of the heart of the capital on Friday, seizing army checkpoints and cutting communications.
The fighting is the heaviest to hit Damascus since July, when a first rebel assault managed to capture several neighbourhoods before a punishing government counteroffensive.
After that rebel foray, the regime quickly reasserted its control over the city, which has spared Damascus much of the violence and destruction the civil war has wrought on other major urban centres.
The rebels and government both consider the fight for Damascus the most likely endgame in a civil war that has already killed more than 60,000 people. The city is heavily fortified and dotted with armed checkpoints, and activists say it is surrounded with three of the most loyal divisions of the army, including the Republican Guard and the feared 4th Division, commanded by Mr Assad's brother Maher.
The latest offensive did not appear to be coordinated with rebels on other sides of the capital, and it was unclear whether the opposition fighters would be able to hold their ground.
Activists said the fighting on Saturday focused on a main highway that leads to northern Syria, a key road the regime uses to move troops and supplies. Rebels cut the road on Friday, and still controlled parts of it on Saturday despite government airstrikes and shelling to try to roll them back, according to Damascus-based activist Maath al Shami.
Activists say the fighting is only the beginning of a long battle for the capital. "The attack was planned for more than 20 days and those responsible for it are army defectors," Mr Shami said. "This is one of the stages to enter the capital. - Storming Damascus is not easy."
He said one checkpoint still stands in the way before the rebels reach Abbasid Square, a landmark plaza in central Damascus.
The Syrian Observatory for Human Rights reported intense air raids on several Damascus suburbs, including Zamalka and Douma, and near the highway. It added that troops shelled the northeastern neighborhoods of Jobar and Qaboun, which have witnessed clashes since Wednesday.
Earlier on Saturday, Mr Assad appointed seven new ministers in a move that appeared to be part of an effort to shore up an economy that has been ravaged by the fighting.