Rebels have been trying for months to capture Aleppo's international airport.
Rami Abdul-Rahman, director of the Britain-based activist group Syrian Observatory for Human Rights, said the fighting is now concentrated around a section of a highway that connects the city with the airport.
The rebels have cut off the highway the army has been using to transport troops and supplies to a military base within the airport complex. The airport east of the city is part of a complex that includes a smaller military airfield and the base.
Rebels have made significant advances in the battle for the complex in the past weeks after capturing two army bases along the road to the airport.
Aleppo is Syria's largest city and its commercial capital. President Bashar Assad's troops have been locked in a stalemate with the rebels there since July, when the city became a major battlefield in the nearly 2-year-old conflict.
The rebels control large swaths of land outside Aleppo and whole neighborhoods inside the city, which is divided between regime- and opposition-controlled areas with both sides shelling each other.
Regime forces fired three missiles into a rebel-held area in eastern Aleppo on Friday, hitting several buildings and killing 29 people, according to the Observatory. The group initially reported 14 casualties in the strike that apparently involved ground-to-ground missiles.
Abdul-Rahman raised the death toll late Friday after activists on the ground said more bodies had been recovered from the rubble of the damaged buildings.
On Saturday, the army pressed an offensive on opposition strongholds outside Damascus, trying to dislodge rebels from areas around the capital which they have been trying to storm for weeks.
Recent rebel advances in the Damascus suburbs, combined with the bombings and three straight days of mortar attacks earlier this week marked the most sustained challenge to the heart of the capital, the seat of Assad's power.
A suicide car bombing on Thursday near the ruling Baath Party headquarters in the heart of Damascus killed 53 civilians and wounded more than 200, according to state media. Anti-regime activists put the death toll at 61, which would make it the deadliest bombing of the revolt in the capital.
The different tolls could not be reconciled.
Nobody claimed responsibility for the attack. Car bombs and suicide attacks have been a hallmark of an Islamic militant group Jabhat al-Nusra fighting among the rebels.
The Nusra fighters have been the most effective group on the battlefield, leading assaults on military installations and controlling whole sections of territory in the north, including parts of Aleppo neighborhoods.
The United Nations says at least 70,000 people have been killed since Syrian conflict started in March 2011.