President Bashar Assad's regime and opposition activists blamed each other for the blackout, which is the first to hit the whole country since Syria's 20-month-old uprising began.
Syrian authorities previously have cut Internet and telephones in areas ahead of military operations.
The Britain-based Syrian Observatory for Human Rights said the main road to Damascus' airport reopened early on Friday afternoon. There were intense clashes after midnight in villages and towns near the airport but the area was calm by the late morning, the group said. It said rebels were able to destroy several army vehicles near the airport.
The Observatory, which has a network of activists around Syria, reported fighting in other southern neighborhoods of Damascus, including Qaboun and Hajar Aswad. The Observatory said it was able to contact its sources who used satellite telephones.
Activists say Assad's regime pulled the plug on the Internet on Thursday, perhaps in preparation for a major offensive. Cellphone service also went out in Damascus and parts of central Syria, they said. The government blamed rebel fighters for the outages.
Thursday's violence appeared to be focused on southern suburbs near the airport, forcing the military to shut the road to the facility. The surrounding districts have been strongholds of rebel support since the uprising began.
With pressure building against the regime on several fronts and government forces on their heels in the battle for the northern commercial hub of Aleppo, rebels have recently begun pushing back into Damascus after largely being driven out of the capital following a July offensive. One Damascus resident reported seeing rebel forces near a suburb of the city previously deemed to be safe from fighting.
The Internet outage, confirmed by two U.S.-based companies that monitor online connectivity, is unprecedented in Syria's uprising against Assad, which activists say has killed more than 40,000 people since the revolt began in March 2011.
Regime forces have suffered a string of tactical defeats in recent weeks, losing air bases and other strategic facilities. The government may be trying to blunt additional rebel offensives by hampering communications.
U.S. State Department spokeswoman Victoria Nuland on Thursday condemned what she called the regime's "assault" on Syrians' ability to communicate with each other and express themselves. She said the move spoke to a desperate attempt by Assad to cling to power.