EgyptAir canceled all further flights to Syria for Monday and Tuesday and will decide later whether to resume flights later in the week, the officials said, speaking on condition of anonymity because they were not authorized to speak to reporters.
EgyptAir had just resumed flights following a three-day suspension because of violence near the airport.
Emirates airlines said on its website that all flights to Syria were suspended "until further notice."
The Britain-based opposition activist group Syrian Observatory for Human Rights said the clashes were within three kilometers (2 miles) of the airport, which lies about 25 kilometers (15 miles) southeast of the city center. The state news service reported clashes in an area about 15 kilometers (9 miles) from the airport. It said nothing about flight cancelations.
More than 40,000 people have been killed since the Syrian revolt started in March last year.
Leaders of Russia — a key supporter of the Assad regime — and opposition ally Turkey discussed disagreements over Syria.
After talks in Istanbul, Russian President Vladimir Putin said that the deployment of NATO antiaircraft missiles along the Turkish border could make the conflict worse.
"Creating a new potential on the border will not settle the situation but rather exacerbate it," he said. "Why would we need more shelling on the border?"
The two countries are firmly enmeshed in Syria's conflict, on opposite sides. Russia continues to back Assad, thrice protecting his regime from censure by the U.N. Security Council. Turkey has called for Assad's ouster and its southern border with Turkey has become a key supply line for rebel forces.
Lebanese security officials said Makdissi, the Foreign Ministry spokesman known for defending Assad crackdown on the opposition as necessary military action against "terrorists," flew from Beirut to London. It was not immediately known whether he had abandoned the regime and he did not respond to phone calls.