Syrian government troops and rebel forces fought Tuesday on the outskirts of Damascus and near the city of Aleppo.
Government aircraft pounded eastern suburbs of the capital and rebel-held areas of Aleppo, the country's commercial hub.
Authorities announced the closure of Aleppo airport because of rebel attacks. The Britain-based Syrian Observatory for Human Rights reported heavy fighting around the base of Syrian army Brigade 80, part of the airport protection force.
Anti-government activists also reported heavy fighting in the Damascus suburb of Daraya, with bombing by Syrian warplanes. Syria's government-run media said troops killed "tens of terrorists" in Daraya and nearby areas.
Syrian rebels are trying to oust President Bashar al-Assad. Activists say 45,000 people have been killed in the conflict that began with peaceful anti-government protests in March 2011.
On Monday, Syria's Prime Minister Wael al-Halaqi said the government was open to talks aimed at solving the conflict. He was responding to U.N.-Arab League envoy Lakhdar Brahimi, who said Sunday he has a plan that is acceptable to world powers.
Brahimi said the plan calls for all sides in Syria to end hostilities, enter into a national dialogue, and form a transitional government leading to new elections. But the plan says nothing about the fate of President Assad, an omission that appears to have stalled its progress.