In the past few weeks, the rebels have stepped up their attacks on airports around Aleppo province, trying to chip away at the government's air power, which poses the biggest obstacle to their advances.
The air force has been bombing and strafing rebel positions and attacking towns under opposition control for months. But the rebels have no planes or effective anti-aircraft weapons to counter the attacks.
The Britain-based Syrian Observatory for Human Rights, an anti-regime activist group, said the fighting around the base of Syrian army Brigade 80, part of a force protecting Aleppo International Airport, led to the closure of the airport late Monday.
"Heavy fighting is taking place around Brigade 80," said Rami Abdul-Rahman, who heads the Observatory. The Observatory relies on a network of activists around Syria.
"The airport has been closed since yesterday," he said.
The Syrian government had no comment on the closing of the airport. On Saturday, Syria's national airline canceled a flight to Aleppo because of fighting nearby.
Rebels have warned that they would target civilian as well as military planes using the Aleppo airport, saying the regime is using civilian planes to bring in supplies and weapons.
The rebels have been attacking three other airports in the Aleppo area, including a military helicopter base near the Turkish border. They have posted dozens of videos online that appear to show fighters shooting mortars, homemade rockets and sniper rifles at targets inside the bases.
There was also heavy fighting in the Damascus suburb of Daraya, southwest of the capital. Daraya is one of the closest suburbs to the capital and is on the edge of two important neighborhoods that are home to a strategic air base and government headquarters.
The fighting in Daraya was so fierce that the explosions echoed in some parts of the capital.
Although the regime still tightly controls much of Damascus, its seat of power, rebels have been posing a stiffer challenge in the suburbs. In the past few weeks, there has been fighting near the capital's international airport that interrupted some flights. The road to the airport, just south of the capital, was also closed during the fighting.
The Observatory and activist Mohammed Saeed, who is based near Damascus, said Syrian warplanes bombed Daraya on Tuesday.
State-run news agency SANA said troops killed "tens of terrorists" in Daraya and nearby areas. The regime refers to rebels as "terrorists."
Activists say more than 45,000 people have been killed since the uprising against Assad began 22 months ago.
Daraya is few miles from the strategic military air base of Mazzeh in a western neighborhood of the capital. It is also on the edge of the Kfar Sousseh neighborhood that is home to the government headquarters, the General Security intelligence agency head office and the Interior Ministry. That ministry was targeted in a recent suicide attack that wounded Interior Minister Mohammed al-Shaar.
"The regime is doing all it can to regain Daraya," said Maath al-Shami, an activist based in the Syrian neighborhood of Mazzeh, via Skype. "The regime is dying to get back it back," he added.
"Daraya is the gate of Damascus for the rebels," said al-Shami.
Amateur videos showed smoke billowing from Daraya from what activists said were the air raids. Another video showed a street covered with debris as fire raged on the second floor of a five-story building.
The videos appeared genuine and corresponded to other AP reporting on the events depicted.
In August, activists reported that between 300 and 600 people were killed in Daraya over several days in a killing spree by troops and pro-regime militiamen who stormed the town after heavy fighting and days of shelling.
The Observatory and al-Shami reported sporadic shelling and clashes in southern neighborhoods of Damascus and the Palestinian refugee camp of Yarmouk on Tuesday. The Observatory said shelling and snipers fire killed two people in Yarmouk and two in another neighborhood.