The clashes, which erupted after midnight yesterday and continued through the day today, also left at least 30 soldiers dead or wounded, said the Britain-based Syrian Observatory for Human Rights. The Syrian government does not publicise its casualties in the war.
President Bashar Assad's forces, backed by Lebanese Hezbollah militants and pro-government militias, have been trying to wrest as much territory as possible from the opposition in Aleppo and elsewhere in Syria ahead of the June 3 presidential elections.
In the city of Aleppo, Syria's largest and its former commercial hub, government forces have been relentlessly shelling opposition districts with aircraft and artillery in recent months.
Today, government aircraft bombed three rebel-held districts in the city, including Masaken Hanano, where at least two people died, the Observatory said. The activist group also reported heavy fighting in Mleiha east of Damascus and airstrikes on the capital's district of Jobar on the edge of the city.
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The rebels have been striking back, firing mortars and makeshift rockets into cities and towns under control of Assad's forces. They have also detonated several car bombs in major cities, including in the capital, Damascus.
The state-run SANA news agency said rockets struck in Aleppo's residential neighbourhood of Ashrafiyeh overnight, killing nine people and wounding several, mostly women and children.
Syria's conflict, which began with largely peaceful protests in March 2011, has evolved into a civil war with sectarian overtones, pitting predominantly Sunni Muslim rebels against Assad's government that is dominated by Alawites, a sect in Shiite Islam. More than 150,000 people have been killed and millions have been displaced by the war.